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Journal articles on the topic 'Parameter estimates'
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1
Mead, J. L. "Discontinuous parameter estimates with least squares estimators." Applied Mathematics and Computation 219, no. 10 (2013): 5210–23. http://dx.doi.org/10.1016/j.amc.2012.11.067.
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Robitzsch, Alexander. "Linking Error Estimation in Fixed Item Parameter Calibration: Theory and Application in Large-Scale Assessment Studies." Foundations 5, no. 1 (2025): 4. https://doi.org/10.3390/foundations5010004.
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In fixed item parameter calibration (FIPC), an item response theory (IRT) model is estimated with item parameters fixed at reference values to estimate the distribution parameters within a specific group. The presence of random differential item functioning (DIF) within this group introduces additional variability in the distribution parameter estimates, which is captured by the linking error (LE). Conventional LE estimates, based on item jackknife methods, are subject to positive bias due to sampling errors. To address this, this article introduces a bias-corrected LE estimate. Moreover, the use of statistical inference is examined using the newly proposed bias-corrected total error, which includes both the sampling error and LE. The proposed error estimates were evaluated through a simulation study, and their application is illustrated using PISA 2006 data for the reading domain.
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Pilling, Graham M., Geoffrey P. Kirkwood, and Stephen G. Walker. "An improved method for estimating individual growth variability in fish, and the correlation between von Bertalanffy growth parameters." Canadian Journal of Fisheries and Aquatic Sciences 59, no. 3 (2002): 424–32. http://dx.doi.org/10.1139/f02-022.
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A new method for estimating individual variability in the von Bertalanffy growth parameters of fish species is presented. The method uses a nonlinear random effects model, which explicitly assumes that an individual's growth parameters represent samples from a multivariate population of growth parameters characteristic of a species or population. The method was applied to backcalculated length-at-age data from the tropical emperor, Lethrinus mahsena. Individual growth parameter variability estimates were compared with those derived using the current "standard" method, which characterizes the joint distribution of growth parameter estimates obtained by independently fitting a growth curve to each individual data set. Estimates of mean von Bertalanffy growth parameters from the two methods were similar. However, estimated growth parameter variances were much higher using the standard method. Using the random effects model, the estimated correlation between population mean values of L[Formula: see text] and K was 0.52 or 0.42, depending on the marginal distribution assumed for K. The latter estimate had a 95% posterior credibility interval of 0.62 to 0.17. These represent the first reliable estimate of this correlation and confirm the view that these parameters are negatively correlated in fish populations; however, the absolute correlation value is somewhat lower than has been assumed.
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Coventry, William L., and Matthew C. Keller. "Estimating the Extent of Parameter Bias in the Classical Twin Design: A Comparison of Parameter Estimates From Extended Twin-Family and Classical Twin Designs." Twin Research and Human Genetics 8, no. 3 (2005): 214–23. http://dx.doi.org/10.1375/twin.8.3.214.
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AbstractThe classical twin design (CTD) circumvents parameter indeterminacy by assuming (1) negligible higher-order epistasis; and (2) either nonadditive genetic or common environmental effects are nonexistent, creating two potential sources of bias (Eaves et al., 1978; Grayson, 1989). Because the extended twin-family design (ETFD) uses many more unique covariance observations to estimate parameters, common environmental and nonadditive genetic parameters can be simultaneously estimated. The ETFD thereby corrects for what is likely to be the largest of the two sources of bias in CTD parameter estimates (Keller & Coventry, 2005). In the current paper, we assess the extent of this and other potential sources of bias in the CTD by comparing all published ETFD parameter estimates to CTD parameter estimates derived from the same data. CTD estimates of the common environment were lower than ETFD estimates of the common environment for some phenotypes, but for other phenotypes (e.g., stature in females and certain social attitudes), what appeared as the common environment was resolved to be assortative mating in the ETFD. On average, CTD estimates of nonadditive genetic factors were 43% lower, and additive genetic factors 63% higher, than ETFD estimates. However, broad-sense heritability estimates from the CTD were only 18% higher than ETFD estimates, highlighting that the CTD is useful for estimating broad-sense but not narrow-sense heritability. These results suggest that CTD estimates can be misleading when interpreted literally, but useful, albeit coarse, when interpreted properly.
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Rajanayaka, Channa, and Don Kulasiri. "Investigation of a parameter estimation method for contaminant transport in aquifers." Journal of Hydroinformatics 3, no. 4 (2001): 203–13. http://dx.doi.org/10.2166/hydro.2001.0019.
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Real world groundwater aquifers are heterogeneous and system variables are not uniformly distributed across the aquifer. Therefore, in the modelling of the contaminant transport, we need to consider the uncertainty associated with the system. Unny presented a method to describe the system by stochastic differential equations and then to estimate the parameters by using the maximum likelihood approach. In this paper, this method was explored by using artificial and experimental data. First a set of data was used to explore the effect of system noise on estimated parameters. The experimental data was used to compare the estimated parameters with the calibrated results. Estimates obtained from artificial data show reasonable accuracy when the system noise is present. The accuracy of the estimates has an inverse relationship to the noise. Hydraulic conductivity estimates in a one-parameter situation give more accurate results than in a two-parameter situation. The effect of the noise on estimates of the longitudinal dispersion coefficient is less compared to the effect on hydraulic conductivity estimates. Comparison of the results of the experimental dataset shows that estimates of the longitudinal dispersion coefficient are similar to the aquifer calibrated results. However, hydraulic conductivity does not provide a similar level of accuracy. The main advantage of the estimation method presented here is its direct dependence on field observations in the presence of reasonably large noise levels.
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Yi, Kyongsu, and Karl Hedrick. "Observer-Based Identification of Nonlinear System Parameters." Journal of Dynamic Systems, Measurement, and Control 117, no. 2 (1995): 175–82. http://dx.doi.org/10.1115/1.2835177.
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This paper deals with an observer-based nonlinear system parameter identification method utilizing repetitive excitation. Although methods for physical parameter identification of both linear and nonlinear systems are already available, they are not attractive from a practical point of view since the methods assume that all the system, x, and the system input are available. The proposed method is based on a “sliding observer” and a least-square method. A sufficient condition for the convergence of the parameter estimates is provided in the case of “Lipschitz” nonlinear second-order systems. The observer is used to estimate signals which are difficult or expensive to measure. Using the estimated states of the system with repetitive excitation, the parameter estimates are obtained. The observer based identification method has been tested on a half car simulation and used to identify the parameters of a half car suspension test rig. The estimates of nonlinear damping coefficients of a vehicle suspension, suspension stiffness, pitch moment inertia, equivalent sprung mass, and unsprung mass are obtained by the proposed method. Simulation and experimental results show that the identifier estimates the vehicle parameters accurately. The proposed identifier will be useful for parameter identification of actual vehicles since vehicle parameters can be identified only using vehicle excitation tests rather than component testing.
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Luo, Yong, and Dimiter M. Dimitrov. "A Short Note on Obtaining Point Estimates of the IRT Ability Parameter With MCMC Estimation in Mplus: How Many Plausible Values Are Needed?" Educational and Psychological Measurement 79, no. 2 (2018): 272–87. http://dx.doi.org/10.1177/0013164418777569.
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Plausible values can be used to either estimate population-level statistics or compute point estimates of latent variables. While it is well known that five plausible values are usually sufficient for accurate estimation of population-level statistics in large-scale surveys, the minimum number of plausible values needed to obtain accurate latent variable point estimates is unclear. This is especially relevant when an item response theory (IRT) model is estimated with MCMC (Markov chain Monte Carlo) methods in Mplus and point estimates of the IRT ability parameter are of interest, as Mplus only estimates the posterior distribution of each ability parameter. In order to obtain point estimates of the ability parameter, a number of plausible values can be drawn from the posterior distribution of each individual ability parameter and their mean (the posterior mean ability estimate) can be used as an individual ability point estimate. In this note, we conducted a simulation study to investigate how many plausible values were needed to obtain accurate posterior mean ability estimates. The results indicate that 20 is the minimum number of plausible values required to obtain point estimates of the IRT ability parameter that are comparable to marginal maximum likelihood estimation(MMLE)/expected a posteriori (EAP) estimates. A real dataset was used to demonstrate the comparison between MMLE/EAP point estimates and posterior mean ability estimates based on different number of plausible values.
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Fieberg, J., and D. F. Staples. "The role of variability and uncertainty in testing hypotheses involving parameters in stochastic demographic models." Canadian Journal of Zoology 84, no. 11 (2006): 1698–701. http://dx.doi.org/10.1139/z06-153.
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Hierarchical / random effect models provide a statistical framework for estimating variance parameters that describe temporal and spatial variability of vital rates in population dynamic models. In practice, estimates of variance parameters (e.g., process error) from these models are often confused with estimates of uncertainty about model parameter estimates (e.g., standard errors). These two sources of “error” have different implications for predictions from stochastic models. Estimates of process error (or variability) are useful for describing the magnitude of variation in vital rates over time and are a feature of the modeled process itself, whereas estimates of parameter standard errors (or uncertainty) are necessary for interpreting how well we are able to estimate model parameters and whether they differ among groups. The goal of this comment is to illustrate these concepts in the context of a recent paper by A.W. Reed and N.A. Slade (Can. J. Zool. 84: 635–642 (2006)) . In particular, we will show that their “hypothesis tests” involving mean parameters are actually comparisons of the estimated distributions of vital rates among groups of individuals.
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Koots, Kenneth R., and John P. Gibson. "Realized Sampling Variances of Estimates of Genetic Parameters and the Difference Between Genetic and Phenotypic Correlations." Genetics 143, no. 3 (1996): 1409–16. http://dx.doi.org/10.1093/genetics/143.3.1409.
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Abstract A data set of 1572 heritability estimates and 1015 pairs of genetic and phenotypic correlation estimates, constructed from a survey of published beef cattle genetic parameter estimates, provided a rare opportunity to study realized sampling variances of genetic parameter estimates. The distribution of both heritability estimates and genetic correlation estimates, when plotted against estimated accuracy, was consistent with random error variance being some three times the sampling variance predicted from standard formulae. This result was consistent with the observation that the variance of estimates of heritabilities and genetic correlations between populations were about four times the predicted sampling variance, suggesting few real differences in genetic parameters between populations. Except where there was a strong biological or statistical expectation of a difference, there was little evidence for differences between genetic and phenotypic correlations for most trait combinations or for differences in genetic correlations between populations. These results suggest that, even for controlled populations, estimating genetic parameters specific to a given population is less useful than commonly believed. A serendipitous discovery was that, in the standard formula for theoretical standard error of a genetic correlation estimate, the heritabilities refer to the estimated values and not, as seems generally assumed, the true population values.
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Jiang, Renyan. "A Quasi-Normal Distribution and its Application in Parameter Estimation on Heavily Censored Data." International Journal of Reliability, Quality and Safety Engineering 28, no. 05 (2021): 2150027. http://dx.doi.org/10.1142/s0218539321500273.
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Parameter estimation on heavily censored data is a challenging issue. This paper addresses this issue using a two-step single-parameter maximum likelihood method to estimate mean time to failure (MTTF) and Weibull shape parameter (WSP). The first step fits the data to three one-parameter auxiliary models, which are special cases of a two-parameter quasi-normal distribution with nonnegative support, to obtain three estimates of the MTTF. The second step estimates the WSP through fixing each of the MTTF estimates. The best estimates are selected from three pairs of estimates based on appropriate rules. A simple numerical method is also proposed to construct the confidence intervals of the estimated MTTF and WSP. The auxiliary models are derived, the model selection rules are specified, and a numerical experiment is carried out to illustrate the accuracy of the proposed method.
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Uzhga Rebrov, Oleg, and Galina Kuleshova. "FUZZY ROBUST ESTIMATES OF LOCATION AND SCALE PARAMETERS OF A FUZZY RANDOM VARIABLE." ENVIRONMENT. TECHNOLOGIES. RESOURCES. Proceedings of the International Scientific and Practical Conference 2 (June 17, 2021): 181–86. http://dx.doi.org/10.17770/etr2021vol2.6566.
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A random variable is a variable whose components are random values. To characterise a random variable, the arithmetic mean is widely used as an estimate of the location parameter, and variation as an estimate of the scale parameter. The disadvantage of the arithmetic mean is that it is sensitive to extreme values, outliers in the data. Due to that, to characterise random variables, robust estimates of the location and scale parameters are widely used: the median and median absolute deviation from the median. In real situations, the components of a random variable cannot always be estimated in a deterministic way. One way to model the initial data uncertainty is to use fuzzy estimates of the components of a random variable. Such variables are called fuzzy random variables. In this paper, we examine fuzzy robust estimates of location and scale parameters of a fuzzy random variable: fuzzy median and fuzzy median of the deviations of fuzzy component values from the fuzzy median.
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Lappi, Juha, and Juha Malinen. "Random-Parameter Height/Age Models when Stand Parameters and Stand Age are Correlated." Forest Science 40, no. 4 (1994): 715–31. http://dx.doi.org/10.1093/forestscience/40.4.715.
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Abstract Height/age curves of dominant trees in a stand can be predicted using models containing random stand and tree parameters. If the population mean curve is estimated from the data where stand-specific parameters are correlated with stand age (e.g., because old stands are growing on poor sites), this correlation may cause biased estimates. The same bias problem occurs in traditional site index methods. It is shown how ordinary least squares estimates of tree specific parameters can be used for computing unbiased estimates of the population mean parameters and for estimating the relationship between stand parameters and stand age. The application of the estimated model several years after the data collection time is problematic because it should be known how the population changes over time. For. Sci. 40(4):715-731.
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Riswan, Riswan. "Sample Size and Test Length for Item Parameter Estimate and Exam Parameter Estimate." Al-Khwarizmi : Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam 9, no. 1 (2021): 69–78. http://dx.doi.org/10.24256/jpmipa.v9i1.2384.
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The Item Response Theory (IRT) model contains one or more parameters in the model. These parameters are unknown, so it is necessary to predict them. This paper aims (1) to determine the sample size (N) on the stability of the item parameter (2) to determine the length (n) test on the stability of the estimate parameter examinee (3) to determine the effect of the model on the stability of the item and the parameter to examine (4) to find out Effect of sample size and test length on item stability and examinee parameter estimates (5) Effect of sample size, test length, and model on item stability and examinee parameter estimates. This paper is a simulation study in which the latent trait (q) sample simulation is derived from a standard normal population of ~ N (0.1), with a specific Sample Size (N) and test length (n) with the 1PL, 2PL and 3PL models using Wingen. Item analysis was carried out using the classical theory test approach and modern test theory. Item Response Theory and data were analyzed through software R with the ltm package. The results showed that the larger the sample size (N), the more stable the estimated parameter. For the length test, which is the greater the test length (n), the more stable the estimated parameter (q).
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Skopintseva, Lyubov, and Alexey Stovas. "Overburden dependent AVA inversion." GEOPHYSICS 75, no. 2 (2010): C15—C23. http://dx.doi.org/10.1190/1.3332529.
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Amplitude-variation-with-offset (AVO) analysis is strongly dependent on interpretation of the estimated traveltime parameters. In practice, we can estimate two or three traveltime parameters that require interpretation within the families of two- or three-parameter velocity models, respectively. Increasing the number of model parameters improves the quality of overburden description and reduces errors in AVO analysis. We have analyzed the effect of two- and three-parameter velocity model interpretation for the overburden on AVO data and have developed error estimates in the reservoir parameters.
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Bellsky, Thomas, Jesse Berwald, and Lewis Mitchell. "Nonglobal Parameter Estimation Using Local Ensemble Kalman Filtering." Monthly Weather Review 142, no. 6 (2014): 2150–64. http://dx.doi.org/10.1175/mwr-d-13-00200.1.
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Abstract The authors study parameter estimation for nonglobal parameters in a low-dimensional chaotic model using the local ensemble transform Kalman filter (LETKF). By modifying existing techniques for using observational data to estimate global parameters, they present a methodology whereby spatially varying parameters can be estimated using observations only within a localized region of space. Taking a low-dimensional nonlinear chaotic conceptual model for atmospheric dynamics as a numerical test bed, the authors show that this parameter estimation methodology accurately estimates parameters that vary in both space and time, as well as parameters representing physics absent from the model.
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Ahmad, W. M. A. W., R. A. A. Rohim, and N. H. Ismail. "Forecasting Parameter Estimates: A Modeling Approach Using Exponential and Linear Regression." Engineering, Technology & Applied Science Research 8, no. 4 (2018): 3162–67. https://doi.org/10.5281/zenodo.1450645.
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This paper supplies a calculation method for the parameter estimates of an exponential equation through SAS algorithm. The aim of this paper is to investigate the efficiency of the gained parameter estimates through the forecasting performance. The proposed calculation method can provide a very useful technique to develop an exponential equation with better accuracy performance. This research paper illustrates a sample of the data obtained from the established study, which characterize the proliferative capacity of mesenchymal stem cells. This paper also provides the specific algorithm for the parameter estimates.
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Bako, Sunday Samuel, Mohd Bakri Adam, and Anwar Fitrianto. "Impact of Dependence on Parameter Estimates of Autoregressive Process with Gumbel Distributed Innovation." MATEMATIKA 34, no. 2 (2018): 365–80. http://dx.doi.org/10.11113/matematika.v34.n2.941.
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Recent studies have shown that independent identical distributed Gaussian random variables is not suitable for modelling extreme values observed during extremal events. However, many real life data on extreme values are dependent and stationary rather than the conventional independent identically distributed data. We propose a stationary autoregressive (AR) process with Gumbel distributed innovation and characterise the short-term dependence among maxima of an (AR) process over a range of sample sizes with varying degrees of dependence. We estimate the maximum likelihood of the parameters of the Gumbel AR process and its residuals, and evaluate the performance of the parameter estimates. The AR process is fitted to the Gumbel-generalised Pareto (GPD) distribution and we evaluate the performance of the parameter estimates fitted to the cluster maxima and the original series. Ignoring the effect of dependence leads to overestimation of the location parameter of the Gumbel-AR (1) process. The estimate of the location parameter of the AR process using the residuals gives a better estimate. Estimate of the scale parameter perform marginally better for the original series than the residual estimate. The degree of clustering increases as dependence is enhance for the AR process. The Gumbel-AR(1) fitted to the Gumbel-GPD shows that the estimates of the scale and shape parameters fitted to the cluster maxima perform better as sample size increases, however, ignoring the effect of dependence lead to an underestimation of the parameter estimates of the scale parameter. The shape parameter of the original series gives a superior estimate compare to the threshold excesses fitted to the Gumbel-GPD.
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Lasslop, G., M. Reichstein, J. Kattge, and D. Papale. "Influences of observation errors in eddy flux data on inverse model parameter estimation." Biogeosciences Discussions 5, no. 1 (2008): 751–85. http://dx.doi.org/10.5194/bgd-5-751-2008.
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Abstract. Eddy covariance data are increasingly used to estimate parameters of ecosystem models and for proper maximum likelihood parameter estimates the error structure in the observed data has to be fully characterized. In this study we propose a method to characterize the random error of the eddy covariance flux data, and analyse error distribution, standard deviation, cross- and autocorrelation of CO2 and H2O flux errors at four different European eddy covariance flux sites. Moreover, we examine how the treatment of those errors and additional systematic errors influence statistical estimates of parameters and their associated uncertainties with three models of increasing complexity – a hyperbolic light response curve, a light response curve coupled to water fluxes and the SVAT scheme BETHY. In agreement with previous studies we find that the error standard deviation scales with the flux magnitude. The previously found strongly leptokurtic error distribution is revealed to be largely due to a superposition of almost Gaussian distributions with standard deviations varying by flux magnitude. The crosscorrelations of CO2 and H2O fluxes were in all cases negligible (R2 below 0.2), while the autocorrelation is usually below 0.6 at a lag of 0.5 hours and decays rapidly at larger time lags. This implies that in these cases the weighted least squares criterion yields maximum likelihood estimates. To study the influence of the observation errors on model parameter estimates we used synthetic datasets, based on observations of two different sites. We first fitted the respective models to observations and then added the random error estimates described above and the systematic error, respectively, to the model output. This strategy enables us to compare the estimated parameters with true parameters. We show that the correct implementation of the random error standard deviation scaling with flux magnitude significantly reduces the parameter uncertainty and often yields parameter retrievals that are closer to the true value, than by using ordinary least squares. The systematic error leads to systematically biased parameter estimates, but its impact varies by parameter. The parameter uncertainty slightly increases, but the true parameter is not within the uncertainty range of the estimate. This means that the uncertainty is underestimated with current approaches that neglect selective systematic errors in flux data. Hence, we conclude that potential systematic errors in flux data need to be addressed more thoroughly in data assimilation approaches since otherwise uncertainties will be vastly underestimated.
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Lasslop, G., M. Reichstein, J. Kattge, and D. Papale. "Influences of observation errors in eddy flux data on inverse model parameter estimation." Biogeosciences 5, no. 5 (2008): 1311–24. http://dx.doi.org/10.5194/bg-5-1311-2008.
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Abstract. Eddy covariance data are increasingly used to estimate parameters of ecosystem models. For proper maximum likelihood parameter estimates the error structure in the observed data has to be fully characterized. In this study we propose a method to characterize the random error of the eddy covariance flux data, and analyse error distribution, standard deviation, cross- and autocorrelation of CO2 and H2O flux errors at four different European eddy covariance flux sites. Moreover, we examine how the treatment of those errors and additional systematic errors influence statistical estimates of parameters and their associated uncertainties with three models of increasing complexity – a hyperbolic light response curve, a light response curve coupled to water fluxes and the SVAT scheme BETHY. In agreement with previous studies we find that the error standard deviation scales with the flux magnitude. The previously found strongly leptokurtic error distribution is revealed to be largely due to a superposition of almost Gaussian distributions with standard deviations varying by flux magnitude. The crosscorrelations of CO2 and H2O fluxes were in all cases negligible (R2 below 0.2), while the autocorrelation is usually below 0.6 at a lag of 0.5 h and decays rapidly at larger time lags. This implies that in these cases the weighted least squares criterion yields maximum likelihood estimates. To study the influence of the observation errors on model parameter estimates we used synthetic datasets, based on observations of two different sites. We first fitted the respective models to observations and then added the random error estimates described above and the systematic error, respectively, to the model output. This strategy enables us to compare the estimated parameters with true parameters. We illustrate that the correct implementation of the random error standard deviation scaling with flux magnitude significantly reduces the parameter uncertainty and often yields parameter retrievals that are closer to the true value, than by using ordinary least squares. The systematic error leads to systematically biased parameter estimates, but its impact varies by parameter. The parameter uncertainty slightly increases, but the true parameter is not within the uncertainty range of the estimate. This means that the uncertainty is underestimated with current approaches that neglect selective systematic errors in flux data. Hence, we conclude that potential systematic errors in flux data need to be addressed more thoroughly in data assimilation approaches since otherwise uncertainties will be vastly underestimated.
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Hac, A., and P. D. Spanos. "Time Domain Method for Parameter System Identification." Journal of Vibration and Acoustics 112, no. 3 (1990): 281–87. http://dx.doi.org/10.1115/1.2930506.
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In this paper a method of parameter identification for a multi-degree-of-freedom structural system in a noisy environment is presented. The method involves an iterative procedure in which initial parameter estimates are obtained by relying on a least squares kind of approximation. This estimate is used in an adaptive Kalman filter to obtain an improved estimate of the system state. The improved estimate is then utilized in the least squares approximation to produce refined estimates of the system parameters. The iteration is repeated until it converges within an acceptable margin. The parameter errors are compensated during filtering by adding pseudonoise to the system equation; the noise itensity is updated in each iteration. Results of a simulation study conducted for a two-degree-of-freedom system indicate that the method can yield, for a relatively low computational cost, reliable estimates of system parameters, even when the data record is short.
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Zala, Cedric A., and John M. Ozard. "Estimation of Geoacoustic Parameters from Narrowband Data Using a Search-Optimization Technique." Journal of Computational Acoustics 06, no. 01n02 (1998): 223–43. http://dx.doi.org/10.1142/s0218396x98000168.
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Geoacoustic parameters were estimated for vertical array data from the matched-field inversion benchmark data sets. Separate inversions were performed for narrowband data at 25 Hz, 50 Hz and 75 Hz, using a matching function consisting of the incoherent sum of the Bartlett outputs for the five vertical arrays at ranges of 1, 2, 3, 4 and 5 km. Parameter estimation was performed using a parabolic equation sound propagation algorithm to generate the replica fields, and a search-optimization technique to obtain estimates of the optimized parameter values. This technique involved an initial search stage in which the parameter space was sampled, and a second optimization stage in which each of a specified number of the best matches found in the search stage was used as the starting point for optimization. This approach provided multiple independent estimates of the geoacoustic parameters, and allowed assessment of the non-uniqueness of the problem and the sensitivity of the matching function to the individual parameters. A method was developed to combine the results for several frequencies to estimate the parameters. It used a weighted average with weights computed on the basis of the relative sensitivities at those frequencies; these sensitivities were estimated by the root-mean-square (RMS) gradient observed during the optimizations. Strong interdependencies among the parameters were found in the analysis, particularly between the sediment thickness and the sound speed at the bottom of the sediment. For the single-frequency matching function used here, it was observed that the inversion problems were ill-posed in that sets of parameter values from a wide region of the parameter space gave essentially perfect matches. The consistency of the parameter estimates was greatly improved by including a regularization term in the matching function. Regularized search-optimization provided an efficient method for estimating an effective geoacoustic model for acoustic field prediction.
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Hollenbach, Florian M., Jacob M. Montgomery, and Adriana Crespo-Tenorio. "Bayesian Versus Maximum Likelihood Estimation of Treatment Effects in Bivariate Probit Instrumental Variable Models." Political Science Research and Methods 7, no. 3 (2018): 651–59. http://dx.doi.org/10.1017/psrm.2018.15.
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Bivariate probit models are a common choice for scholars wishing to estimate causal effects in instrumental variable models where both the treatment and outcome are binary. However, standard maximum likelihood approaches for estimating bivariate probit models are problematic. Numerical routines in popular software suites frequently generate inaccurate parameter estimates and even estimated correctly, maximum likelihood routines provide no straightforward way to produce estimates of uncertainty for causal quantities of interest. In this note, we show that adopting a Bayesian approach provides more accurate estimates of key parameters and facilitates the direct calculation of causal quantities along with their attendant measures of uncertainty.
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Mohamed, M., and N. Joy. "Lateral directional aircraft aerodynamic parameter estimation using adaptive stochastic nonlinear filter." Aeronautical Journal 125, no. 1294 (2021): 2217–28. http://dx.doi.org/10.1017/aer.2021.61.
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AbstractThis paper aims to accurately estimate the lateral directional aerodynamic parameters in real time irrespective of the variations in the process and measurement covariance matrices. The proposed algorithm for parameter estimation is based on the integration of adaptive techniques into a stochastic nonlinear filter. The proposed adaptive estimation algorithm is applied to flight test data, and the lateral directional derivatives are estimated in real time. The estimates are compared with those obtained from the Filter Error Method (FEM), an offline parameter estimation method accounting for process noise. The estimation results are observed to be very comparable, and the supremacy of the adaptive filter is illustrated by varying the covariance matrices of both process and measurement noises. The parameters estimated by the adaptive filter are found to converge to their actual values, whereas the estimates of the regular filter are observed to diverge from the actual values when changing the noise covariance matrices. The proposed adaptive algorithm can estimate the lateral directional aerodynamic derivatives more accurately without prior knowledge of either process or measurement noise covariance matrices. Hence, it is of great value in online implementations.
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Jacquez, J. A., and T. Perry. "Parameter estimation: local identifiability of parameters." American Journal of Physiology-Endocrinology and Metabolism 258, no. 4 (1990): E727—E736. http://dx.doi.org/10.1152/ajpendo.1990.258.4.e727.
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For biological systems one often cannot set up experiments to measure all of the state variables. If only a subset of the state variables can be measured, it is possible that some of the system parameters cannot influence the measured state variables or that they do so in combinations that do not define the parameters' effects separately. Such parameters are unidentifiable and are in theory unestimable. Given a model of the system, linear or nonlinear, and initial estimates of the values of all parameters, we exhibit a simple theory and describe a program for checking the local identifiability of the parameters at the initial estimates for given experiments on the model. The program, IDENT, is available from the authors.
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Epstein, Michael P., Xihong Lin, and Michael Boehnke. "Ascertainment-Adjusted Parameter Estimates Revisited." American Journal of Human Genetics 70, no. 4 (2002): 886–95. http://dx.doi.org/10.1086/339517.
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Parrilo, Pablo A., and Lennart Ljung. "Initialization of Physical Parameter Estimates." IFAC Proceedings Volumes 36, no. 16 (2003): 1483–88. http://dx.doi.org/10.1016/s1474-6670(17)34969-8.
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Roukema, B. F., Z. Buliński, and N. E. Gaudin. "Poincaré dodecahedral space parameter estimates." Astronomy & Astrophysics 492, no. 3 (2008): 657–73. http://dx.doi.org/10.1051/0004-6361:200810685.
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Kjeldsen, Thomas R., and David A. Jones. "Sampling variance of flood quantiles from the generalised logistic distribution estimated using the method of L-moments." Hydrology and Earth System Sciences 8, no. 2 (2004): 183–90. http://dx.doi.org/10.5194/hess-8-183-2004.
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Abstract. The method of L-moments is the recommended method for fitting the three parameters (location, scale and shape) of a Generalised Logistic (GLO) distribution when conducting flood frequency analyses in the UK. This paper examines the sampling uncertainty of quantile estimates obtained using the GLO distribution for single site analysis using the median to estimate the location parameter. Analytical expressions for the mean and variance of the quantile estimates were derived, based on asymptotic theory. This has involved deriving expressions for the covariance between the sampling median (location parameter) and the quantiles of the estimated unit-median GLO distribution (growth curve). The accuracy of the asymptotic approximations for many of these intermediate results and for the quantile estimates was investigated by comparing the approximations to the outcome of a series of Monte Carlo experiments. The approximations were found to be adequate for GLO shape parameter values between –0.35 and 0.25, which is an interval that includes the shape parameter estimates for most British catchments. An investigation into the contribution of different components to the total uncertainty showed that for large returns periods, the variance of the growth curve is larger than the contribution of the median. Therefore, statistical methods using regional information to estimate the growth curve should be considered when estimating design events at large return periods. Keywords: flood frequency analysis, Flood Estimation Handbook, single site, annual maximum series, Generalised Logistic Distribution, uncertainty
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Beltracchi, T. J., and G. A. Gabriele. "A Recursive Quadratic Programming Based Method for Estimating Parameter Sensitivity Derivatives." Journal of Mechanical Design 113, no. 4 (1991): 487–94. http://dx.doi.org/10.1115/1.2912809.
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Parameter sensitivity analysis is defined as the estimation of changes in the modeling functions and design point due to small changes in the fixed parameters of the formulation. There are currently several methods for estimating parameter sensitivities which either require second order information, or do not return reliable estimates for the derivatives. This paper presents a method based on the use of the recursive quadratic programming method in conjunction with differencing formulas to estimate parameter sensitivity derivatives without the need to calculate second order information. In addition, a modified variable metric method for estimating the Hessian of the Lagrangian function is presented that is used to increase the accuracy of the sensitivity derivatives. Testing is performed on a set of problems with Hessians obtained analytically, and on a set of engineering related problems whose derivatives must be estimated numerically. The results indicate that the method provides good estimates of the parameter sensitivity derivatives on both test sets.
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Okumu, Otieno Kevin, Omondi Joseph Ouno, Anthony Nyutu Karanjah, and Samuel Nganga Muthiga. "Three-parameters Gumbel Distribution: Formulation and Parameter Estimation." International Journal of Statistical Distributions and Applications 10, no. 2 (2024): 25–37. http://dx.doi.org/10.11648/j.ijsd.20241002.12.
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Modeling extreme value theories is really gaining interest in the world with scientist working to improve the flexibility of the distributions by adding parameter(s). Extreme value distributions are always described to include families of Gumbel, Weibull and Frechet distributions. Of the three distributions, Gumbel distribution is the most commonly used in the extreme value theory analysis. Existing literature has shown that the addition of parameter to a distribution makes it robust and/or more flexible hence the study intends to improve the existing two parameters Gumbel distribution using the Marshall and Olkin proposed method for introducing a new estimator/parameter to an existing distribution. The developed distribution will be important to the applications in some life time studies like high temperature, earthquakes, network designs, horse racing, queues in supermarket, insurance, winds, risk management, ozone concentration, flood, engineering and financial concepts. The parameters for the introduced distribution was estimated using Maximum Likelihood Estimation method. The introduced three parameters Gumbel distribution is a probability distribution function which can be used in modelling statistical data. The maximum likelihood estimates for the three parameters namely shape, location and dispersion are efficient, sufficient and consistent and this makes the function more flexible and better for application. The three parameters Gumbel distribution can be used in modeling and analysis of normal data, skewed data and extreme data since it will provide efficient, sufficient and consistent estimates.
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Chandran, K., Z. Hu, and B. F. Smets. "Applicability of an extant batch respirometric assay in describing dynamics of ammonia and nitrite oxidation in a nitrifying bioreactor." Water Science and Technology 52, no. 10-11 (2005): 503–8. http://dx.doi.org/10.2166/wst.2005.0729.
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Several techniques have been proposed for biokinetic estimation of nitrification. Recently, an extant respirometric assay has been presented that yields kinetic parameters for both nitrification steps with minimal physiological change to the microorganisms during the assay. Herein, the ability of biokinetic parameter estimates from the extant respirometric assay to adequately describe concurrently obtained NH4+-N and NO2−-N substrate depletion profiles is evaluated. Based on our results, in general, the substrate depletion profiles resulted in a higher estimate of the maximum specific growth rate coefficient, μmax for both NH4+-N to NO2−-N oxidation and NO2−-N to NO3−-N oxidation compared to estimates from the extant respirograms. The trends in the kinetic parameter estimates from the different biokinetic estimation techniques are paralleled in the nature of substrate depletion profiles obtained from best-fit parameters. Based on a visual inspection, in general, best-fit parameters from optimally designed complete respirograms provided a better description of the substrate depletion profiles than estimates from isolated respirograms. Nevertheless, the sum of the squared errors for the best-fit respirometry based parameters was outside the 95% joint confidence interval computed for the best-fit substrate depletion based parameters. Notwithstanding the difference in kinetic parameter estimates determined in this study, the different biokinetic estimation techniques still are close to estimates reported in literature. Additional parameter identifiability and sensitivity analysis of parameters from substrate depletion assays revealed high precision of parameters and high parameter correlation. Although biokinetic estimation via automated extant respirometry is far more facile than via manual substrate depletion measurements, additional sensitivity analyses are needed to test the impact of differences in the resulting parameter values on continuous reactor performance.
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Badarisam, Fatin Najihah, Mohd Syazwan Mohamad Anuar, Abdul Ghapor Hussin, Adzhar Rambli, and Nurul Raudhah Zulkifli. "Confidence Interval for Parameters Estimates in Circular Simultaneous Functional Relationship Model (CSFRM) for Equal Variances using Normal Asymptotic and Bootstrap Confidence Intervals." Sains Malaysiana 51, no. 11 (2021): 3819–27. http://dx.doi.org/10.17576/jsm-2022-5111-25.
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Few studies have considered the functional relationship model for circular variables. Anuar has proposed a new model of Circular Simultaneous Functional Relationship Model for equal variances. However, the confidence interval for all parameter estimates in this model has not received any consideration in any literature. This paper proposes the confidence interval for all parameter estimates of von Mises distribution in this model. The parameters are estimated using minimum sum (ms) and polyroot function provided in (built-in package) Splus statistical software. The parameters confidence may be obtained from parameter estimation. Those estimation values are obtained by minimizing the negative value of the log-likelihood function. Then, the confidence interval for all parameters based on the bootstrap method will be compared with the normal asymptotic confidence interval via simulation studies. It is found that bootstrap method is the superior method by measuring the performance using coverage probability and expected length. The confidence intervals are illustrated using real wind direction data of Bayan Lepas that collected at 16.3 m above ground level, latitude 05°18’N and longitude 100°16’E. The results showed that the estimate parameters fall between the estimate interval, and we note that the method works well for this model.
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Otunuga, Olusegun Michael. "Time Varying Parameter Estimation Scheme for a Linear Stochastic Differential Equation." International Journal of Statistics and Probability 6, no. 5 (2017): 84. http://dx.doi.org/10.5539/ijsp.v6n5p84.
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In this work, an attempt is made to estimate time varying parameters in a linear stochastic differential equation. By defining $m_{k}$ as the local admissible sample/data observation size at time $t_{k}$, parameters and state at time $t_{k}$ are estimated using past data on interval $[t_{k-m_{k}+1}, t_{k}]$. We show that the parameter estimates at each time $t_{k}$ converge in probability to the true value of the parameters being estimated. A numerical simulation is presented by applying the local lagged adapted generalized method of moments (LLGMM) method to the stochastic differential models governing prices of energy commodities and stock price processes.
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Konečná, Tereza, and Zuzana Hübnerová. "Asymptotic Comparison of Parameters Estimates of Two-parameter Weibull Distribution." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 67, no. 1 (2019): 253–63. http://dx.doi.org/10.11118/actaun201967010253.
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The Weibull distribution is frequently applied in various fields, ranging from economy, business, biology, to engineering. This paper aims at estimating the parameters of two-parameter Weibull distribution are determined. For this purpose, the method of quantiles (three different choices of quantiles) and Weibull probability plot method is utilized. The asymptotic covariance matrix of the parameter estimates is derived for both methods. For optimal random choices of quantiles, the variance, covariance and generalized variance is computed. The main contribution of this study is the introduction of the best choice of percentiles for the method of quantiles and the joint asymptotic efficiency comparison of applied methods.
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Nizeyimana, Pacifique, Kyeong Eun Lee, and Gwangseob Kim. "Bayesian Estimation of Neyman–Scott Rectangular Pulse Model Parameters in Comparison with Other Parameter Estimation Methods." Water 16, no. 17 (2024): 2515. http://dx.doi.org/10.3390/w16172515.
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Neyman–Scott rectangular pulse is a stochastic rainfall model with five parameters. The impacts of initial values and optimization methods on the parameter estimation of the Neyman–Scott rectangular pulse model were investigated using both the method of moments and the method of maximum likelihood. The estimates using the method of moments were influenced by the optimization method and were sensitive to the initial values and the aggregation scale of the data. Thus, by using frequentist estimation methods, we cannot guarantee the unique values as estimates. The aim of this study is to find more reliable unique values as estimates using a Bayesian approach. In this approach, parameters are estimated from the posterior distribution, and model performance is assessed by comparing observed values with fitted values. Slice sampling within the Gibbs sampler algorithm demonstrates superior convergence and model fitting, yielding unique estimates for the model parameters. The main conclusion of this study is that Bayesian estimation methods outperform other estimation methods in terms of providing reliable and stable estimates that improve rainfall generation accuracy.
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Todini, E. "Influence of parameter estimation uncertainty in Kriging: Part 1 - Theoretical Development." Hydrology and Earth System Sciences 5, no. 2 (2001): 215–23. http://dx.doi.org/10.5194/hess-5-215-2001.
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Abstract. This paper deals with a theoretical approach to assessing the effects of parameter estimation uncertainty both on Kriging estimates and on their estimated error variance. Although a comprehensive treatment of parameter estimation uncertainty is covered by full Bayesian Kriging at the cost of extensive numerical integration, the proposed approach has a wide field of application, given its relative simplicity. The approach is based upon a truncated Taylor expansion approximation and, within the limits of the proposed approximation, the conventional Kriging estimates are shown to be biased for all variograms, the bias depending upon the second order derivatives with respect to the parameters times the variance-covariance matrix of the parameter estimates. A new Maximum Likelihood (ML) estimator for semi-variogram parameters in ordinary Kriging, based upon the assumption of a multi-normal distribution of the Kriging cross-validation errors, is introduced as a mean for the estimation of the parameter variance-covariance matrix. Keywords: Kriging, maximum likelihood, parameter estimation, uncertainty
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Baneh, Hasan, Mojtaba Najafi, and Ghodrat Rahimi. "Genetic parameter estimates for early growth traits in Naeini goat." Animal Production Science 52, no. 11 (2012): 1046. http://dx.doi.org/10.1071/an12045.
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The present study was carried out to estimate variance components for growth traits in Naeini goats. Bodyweight records were collected for two flocks under supervision of the Agriculture Organisation of the Esfahan province between 2000 and 2007. Investigated traits were birthweight (BW; n = 2483), weaning weight (WW; n = 1211) and average daily gain from birth to weaning (ADG; n = 1211). Environmental effects were investigated using fixed-effect models, while (co)variance components and genetic parameters were estimated with single- and three-trait analyses using REML methods and WOMBAT software. Six different animal models were fitted to the traits, with the best model for each trait determined by log-likelihood ratio tests (LRT). All traits were significantly influenced by herd, birth year, sex of the kid, birth type and dam age (P < 0.01). On the basis of LRT, maternal permanent environmental effects (c2) were significant for WW and ADG, while BW was affected only by direct genetic effects. Direct heritability estimates for BW, WW and ADG were 0.25 ± 0.05, 0.07 ± 0.06 and 0.21 ± 0.11, respectively. The estimate of c2 was 0.16 ± 0.06 for both WW and ADG. Estimates of genetic correlation for BW–ADG, BW–WW and ADG–WW were 0.49, 0.61 and 0.94, respectively. The estimated phenotypic correlations were positive and were between 0.03 (BW–ADG) and 0.95 (ADG–WW). These results indicate that selection can be used to improve growth traits in this goat breed.
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Faladiba, Muthia Nadhira, and Atina Ahdika. "BAYES ESTIMATION OF EXPONENTIALLY DISTRIBUTED SURVIVAL DATA UNDER SYMMETRIC AND ASYMMETRIC LOSS FUNCTIONS." BAREKENG: Jurnal Ilmu Matematika dan Terapan 18, no. 2 (2024): 0973–86. http://dx.doi.org/10.30598/barekengvol18iss2pp0973-0986.
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In a research study, population data are often not available, so the population parameter is unknown. Meanwhile, knowledge about the population parameter is needed to know the characteristics of the studied population. Therefore, it is needed to estimate the parameter of the population which can be estimated by sample data. There are several methods of parameter estimation which are generally classified into classical and Bayesian method. This research studied the Bayesian parameter estimation method to determine the parameters of the exponentially distributed survival data associated with the reliability measure of the estimates under symmetric and asymmetric loss functions for complete sample data in a closed form. The symmetric loss functions used in this research are Squared Error Loss Function (SELF) and Minimum Expected Loss Function (MELF). The asymmetric loss functions used are the General Entropy Loss Function (GELF) and Linex Loss Function (LLF). Performance of some loss functions used in this research are then compared through numerical simulation to select the best loss function in determining the parameter estimation of the exponentially distributed survival data. We also studied which loss function is best for underestimation and overestimation modeling. Based on simulation results, the Bayes estimates using MELF is the best method to estimate population parameters of the exponentially distributed survival data for the overestimation modeling, while LLF is the best for the underestimation modeling. We provided direct application in a case study of fluorescence lamp survival data. The results show that the best method to estimate the parameter of the standard fluorescence life data is using LLF for underestimation with and MELF for overestimation with .
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Eberhardt, L. L., B. M. Blanchard, and R. R. Knight. "Population trend of the Yellowstone grizzly bear as estimated from reproductive and survival rates." Canadian Journal of Zoology 72, no. 2 (1994): 360–63. http://dx.doi.org/10.1139/z94-049.
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The trend of the Yellowstone grizzly bear (Ursus arctos horribilis) population was estimated using reproductive rates calculated from 22 individual females and survival rates from 400 female bear-years. The point estimate of the rate of increase was 4.6%, with 95% confidence limits of 0 and 9%. Caution in interpreting this result is advised because of possible biases in the population parameter estimates. The main prospects for improving present knowledge of the population trend appear to be further study of possible biases in the parameter estimates, and the continued use of radiotelemetry to increase the number of samples on which the estimates are based.
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Mohamed, Majeed, and Vikalp Dongare. "Aircraft neural modeling and parameter estimation using neural partial differentiation." Aircraft Engineering and Aerospace Technology 90, no. 5 (2018): 764–78. http://dx.doi.org/10.1108/aeat-02-2016-0021.
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Purpose The purpose of this paper is to build a neural model of an aircraft from flight data and online estimation of the aerodynamic derivatives from established neural model. Design/methodology/approach A neural model capable of predicting generalized force and moment coefficients of an aircraft using measured motion and control variable is used to extract aerodynamic derivatives. The use of neural partial differentiation (NPD) method to the multi-input-multi-output (MIMO) aircraft system for the online estimation of aerodynamic parameters from flight data is extended. Findings The estimation of aerodynamic derivatives of rigid and flexible aircrafts is treated separately. In the case of rigid aircraft, longitudinal and lateral-directional derivatives are estimated from flight data. Whereas simulated data are used for a flexible aircraft in the absence of its flight data. The unknown frequencies of structural modes of flexible aircraft are also identified as part of estimation problem in addition to the stability and control derivatives. The estimated results are compared with the parameter estimates obtained from output error method. The validity of estimates has been checked by the model validation method, wherein the estimated model response is matched with the flight data that are not used for estimating the derivatives. Research limitations/implications Compared to the Delta and Zero methods of neural networks for parameter estimation, the NPD method has an additional advantage of providing the direct theoretical insight into the statistical information (standard deviation and relative standard deviation) of estimates from noisy data. The NPD method does not require the initial value of estimates, but it requires a priori information about the model structure of aircraft dynamics to extract the flight stability and control parameters. In the case of aircraft with a high degree of flexibility, aircraft dynamics may contain many parameters that are required to be estimated. Thus, NPD seems to be a more appropriate method for the flexible aircraft parameter estimation, as it has potential to estimate most of the parameters without having the issue of convergence. Originality/value This paper highlights the application of NPD for MIMO aircraft system; previously it was used only for multi-input and single-output system for extraction of parameters. The neural modeling and application of NPD approach to the MIMO aircraft system facilitate to the design of neural network-based adaptive flight control system. Some interesting results of parameter estimation of flexible aircraft are also presented from established neural model using simulated data as a novelty. This gives more value addition to analyzing the flight data of flexible aircraft as it is a challenging problem in parameter estimation of flexible aircraft.
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Godinez, Humberto C., Jon M. Reisner, Alexandre O. Fierro, Stephen R. Guimond, and Jim Kao. "Determining Key Model Parameters of Rapidly Intensifying Hurricane Guillermo (1997) Using the Ensemble Kalman Filter." Journal of the Atmospheric Sciences 69, no. 11 (2012): 3147–71. http://dx.doi.org/10.1175/jas-d-12-022.1.
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Abstract In this work the authors determine key model parameters for rapidly intensifying Hurricane Guillermo (1997) using the ensemble Kalman filter (EnKF). The approach is to utilize the EnKF as a tool only to estimate the parameter values of the model for a particular dataset. The assimilation is performed using dual-Doppler radar observations obtained during the period of rapid intensification of Hurricane Guillermo. A unique aspect of Guillermo was that during the period of radar observations strong convective bursts, attributable to wind shear, formed primarily within the eastern semicircle of the eyewall. To reproduce this observed structure within a hurricane model, background wind shear of some magnitude must be specified and turbulence and surface parameters appropriately specified so that the impact of the shear on the simulated hurricane vortex can be realized. To identify the complex nonlinear interactions induced by changes in these parameters, an ensemble of model simulations have been conducted in which individual members were formulated by sampling the parameters within a certain range via a Latin hypercube approach. The ensemble and the data, derived latent heat and horizontal winds from the dual-Doppler radar observations, are utilized in the EnKF to obtain varying estimates of the model parameters. The parameters are estimated at each time instance, and a final parameter value is obtained by computing the average over time. Individual simulations were conducted using the estimates, with the simulation using latent heat parameter estimates producing the lowest overall model forecast error.
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Villa-Diharce, Enrique R., Miguel Á. Cisneros-Mata, and Evlin A. Ramírez-Félix. "Effects of misrepresentative length samples on individual growth and stock condition estimates." Scientia Marina 87, no. 2 (2023): e062. http://dx.doi.org/10.3989/scimar.05313.062.
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Despite its importance in fisheries studies, there is insufficient understanding on the effect of sampling error or bias on individual growth and other stock indicators. We show the influence of sample length distributions on parameter estimates, illustrating with an example. For the brown swimming crab, we simulated length samples in five configurations and estimated parameters of von Bertalanffy (k, L∞L∞ , t0), asymptotic weight ( W∞W∞ ), weight-length relationship (a, b), growth performance (ϕ’) and condition factor (Kn). Parameter estimates were compared with baseline values using relative bias, standard error and root mean square error. The results show that the accuracy and bias of parameter estimates depend on the lengths sampled. For example, the bias and accuracy of L∞L∞ and W∞W∞ vary inversely with sampled length, whereas combining length segments yields smaller biases of k and t0 than those of L∞L∞ and W∞W∞ . In general, the accuracy of parameter estimates does not always depend on sampling the entire length range, and errors are not the same for all parameters. These results are useful to guide sampling when resources are scarce. We discuss potential reasons for incomplete length sample structure and offer recommendations to obtain best estimates for parameters of interest.
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Mikhailov, V. S. "A simple criterion for the effectiveness of biased estimators." Dependability 24, no. 1 (2024): 25–33. http://dx.doi.org/10.21683/1729-2646-2024-24-1-25-33.
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Point estimation is one of the most common forms of statistical inference. This paper touches upon the concepts of unbiasedness and effectiveness of biased estimates. An attractive approximation for the true (quantitative) value of the estimated parameter t whose values belong to a certain numerical set t T is an estimate , for which the sum of the mathematical expectation of the square of the differences between the possible realization of and the estimated parameter t is minimal (least squares estimation). Another approach is to find the value of the parameter t based on the sum of the mathematical expectation of the difference between the possible realisation ϵ = xi and the estimated parameter t, provided that this sum is zero, so that the positive and negative differences are balanced ∑(xi – t) = 0. Implementations of N independent random values have a general distribution that depends on the estimated parameter t. There are other approaches, but at present there is no single convincing definition of the optimality of finding effective estimates. The well-known statistician Box wrote: “All models are wrong, some are useful.” It is not always easy to establish the adequacy of a model, so our choice is defined by its utility! The simple effectiveness criterion of biased estimates given below is too convenient, however this does not mean that the assumption of the effectiveness of biased estimates based on this criterion is true, yet the usefulness of this simple and convenient model is obvious. The Aim of the paper. The paper aims to construct a simple effectiveness criterion of biased estimates and obtain simple effective estimates of dependability indicators for a binomial test plan and a test plan with limited time and recovery using the constructed simple effectiveness criterion of biased estimates. Conclusions. A simple effectiveness criterion of biased estimates was obtained that compensates for the effect of unequal dispersion values and the square of the bias. New effective biased estimates of various dependability indicators were obtained for a binomial test plan and a plan with limited test time and recovery of failed items.
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Durban, J. W., D. A. Elston, X. Lambin, and P. M. Thompson. "A role for Bayesian inference in cetacean population assessment." J. Cetacean Res. Manage. 2, no. 2 (1999): 117–23. http://dx.doi.org/10.47536/jcrm.v2i2.495.
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Decisions concerning the management and conservation of cetacean populations depend upon knowledge of population parameters, which generally must be estimated from sample data using statistical models. However, data from the cetacean populations are often sparse, and resultant parameter estimates can be uncertain and difficult to obtain. This review uses examples from published work to highlight the utility of the Bayesian statistical paradigm as a suitable estimation framework in these situations. By evaluating the probability of obtaining the available data, given a specified estimator model, for a whole prior distribution of possible parameter values, the Bayesian approach is capable of quantifying the uncertainty associated with parameter estimates. The potential also exists for reducing uncertainty by incorporating relevant information into the prior distributions used in the Bayesian estimation procedure. The paper describes how the use of graphical model specification and graphical output of parameter estimates can make Bayesian methods attractive for data analysis and explains the recent advances in computational methods that have made Bayesian techniques more available for providing useful estimates of cetacean population parameters.
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Rowling, K. R., and DD Reid. "Effect of temporal changes in size composition on estimates of von Bertalanffy growth parameters for Gemfish, Rexa solandri (Cuvier), Gempylidae." Marine and Freshwater Research 43, no. 5 (1992): 1229. http://dx.doi.org/10.1071/mf9921229.
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Estimates of von Bertalanffy growth parameters were made for mature (>3-year-old) gemfish (Rexea solandri), using otoliths sampled biennially from commercial catches between 1980 and 1986. During this period, there was a significant decline in the mean length of mature gemfish in the catch. Large variations in growth-parameter estimates were found over the period sampled (e.g. L∞ ranged between 87.3 and 130.3 cm for males and between 113.1 and 134.7 cm for females). Likelihood-ratio tests showed many of the growth-parameter estimates to be significantly different between the years sampled. Inclusion in the analyses of data for juvenile (1- to 3-year-old) fish considerably reduced both the standard errors of the parameter estimates and the significance of the variations between them. Comparison of parameters estimated by following the growth of individual cohorts spawned in 1975 and 1981 suggested that the variations in the parameters for the 1980-86 data were caused by differences in the length composition of the samples rather than by changes in the growth rate of the fish. The results suggest the need for care when comparing growth parameters estimated for different populations, especially when there are large differences in length composition. The best estimates of growth parameters for gemfish were considered to be those derived from the aggregate data for the whole of the period sampled, including the data for juveniles. For male gemfish these best estimates (with asymptotic standard errors in parentheses) were L∞ =97.5 (0.8) cm, K=0.212 (0.005) year-1 and to = - 0.54 (0.05) years, and for females the estimates were L∞ = 109.4 (0.6) cm, K= 0.180 (0.003) year-1 and to= -0.63 (0.04) years. Likelihood-ratio tests showed these estimates of L∞ and K to be significantly different between the sexes.
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Shawkat, Lina, and Qutaiba Nayef. "A Comparison between (ECM) and (KNN) Methods for the Multivariate skew-normal model with incomplete data." Journal of Al-Rafidain University College For Sciences ( Print ISSN: 1681-6870 ,Online ISSN: 2790-2293 ), no. 1 (October 1, 2021): 377–93. http://dx.doi.org/10.55562/jrucs.v46i1.89.
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Statistical parameter estimation for multivariate data leads to waste of information, if the missing data are omitted, and in return will lead to inaccurate estimates, that is why incomplete data should be estimated using one of the statistical estimation methods to get accurate results and in return good estimates for the parameters. This paper aims to estimate the missing values for a multivariate skew normal model using the Expectation Conditional Maximization (ECM) algorithm and the K-Nearest Neighbour (KNN) method. After estimating the missing values, the model parameters will be estimated using the Maximum Likelihood Estimation (MLE) method and Newton-Raphson algorithm. A comparison between the (ECM) algorithm and the (KNN) method was conducted using the Mean Squared Error (MSE) for the model through simulation to find the best estimation method.
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Okasha, Hassan M., Heba S. Mohammed, and Yuhlong Lio. "E-Bayesian Estimation of Reliability Characteristics of a Weibull Distribution with Applications." Mathematics 9, no. 11 (2021): 1261. http://dx.doi.org/10.3390/math9111261.
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Given a progressively type-II censored sample, the E-Bayesian estimates, which are the expected Bayesian estimates over the joint prior distributions of the hyper-parameters in the gamma prior distribution of the unknown Weibull rate parameter, are developed for any given function of unknown rate parameter under the square error loss function. In order to study the impact from the selection of hyper-parameters for the prior, three different joint priors of the hyper-parameters are utilized to establish the theoretical properties of the E-Bayesian estimators for four functions of the rate parameter, which include an identity function (that is, a rate parameter) as well as survival, hazard rate and quantile functions. A simulation study is also conducted to compare the three E-Bayesian and a Bayesian estimate as well as the maximum likelihood estimate for each of the four functions considered. Moreover, two real data sets from a medical study and industry life test, respectively, are used for illustration. Finally, concluding remarks are addressed.
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Gimenez, O., A. Villefont, E. A. Catchpole, R, Choquet, and B. J. T. Morgan. "Methods for investigating parameter redundancy." Animal Biodiversity and Conservation 27, no. 1 (2004): 561–72. http://dx.doi.org/10.32800/abc.2004.27.0561.
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The quantitative study of marked individuals relies mainly on the use of meaningful biological models. Classical inference is then conducted based on the model likelihood, parameterized by parameters such as survival, recovery, transition and recapture probabilities. In classical statistics, we seek parameter estimates by maximising the likelihood. However, models are often overparameterized and, as a consequence, some parameters cannot be estimated separately. Identifying how many and which (functions of) parameters are estimable is thus crucial not only for proper model selection based upon likelihood ratio tests or information criteria but also for the interpretation of the estimates obtained. In this paper, we provide the reader with a description of the tools available to check for parameter redundancy. We aim to assist people in choosing the most appropriate method to solve their own specific problems.
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Kim, Seonghoon. "Estimation of Asymptotic Standard Errors of Bayesian Modal Item Parameter Estimators: Application to the 2PL and 3PL Models." Korean Society for Educational Evaluation 38, no. 1 (2025): 143–78. https://doi.org/10.31158/jeev.2025.38.1.143.
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Item parameters of item response theory (IRT) models are often estimated by the Bayesian modal (BM) method, which is an extension of the marginal maximum likelihood (MML) method. The purpose of this study is to present a general method to estimate the asymptotic standard errors (SEs) of MML or BM item parameter estimators and to examine its specific performance under the two-parameter logistic (2PL) and three-parameter logistic (3PL) models. The asymptotic SEs of BM item parameter estimators can be computed theoretically based on the posterior information matrix. Before examining the performance of the SE estimation method presented, the methods used by the BILOG-MG and PARSCALE programs for estimating the SEs of MML/BM item parameter estimates were diagnosed using the SE estimation formulas presented. To examine the performance of the proposed SE estimation method, computer simulations were conducted. For the 2PL and 3PL model tests, the theoretical asymptotic SE tended to be larger than the empirical SE (the standard deviation of item parameter estimates from replications of simulation). For the 2PL model test, this tendency (the asymptotic SEs being overestimated against the empirical SEs) was negligible when the sample size increased to 2,000. For the 3PL model test, this tendency was still observed even at the 2,000 sample size, remarkably for the pseudo-guessing parameters of very easy items.
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Dallil, Ahmed, and Abdelaziz Ouldali. "Polynomial phase signal parameter estimates refinement." IET Radar, Sonar & Navigation 13, no. 3 (2019): 492–95. http://dx.doi.org/10.1049/iet-rsn.2018.5047.
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