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Journal articles on the topic 'Estimation by Method of Moments'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Kuersteiner, Guido M., and Laszlo Matyas. "Generalized Method of Moments Estimation." Journal of the American Statistical Association 95, no. 451 (September 2000): 1014. http://dx.doi.org/10.2307/2669498.

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2

Rao, K. Srinivasa. "Estimation of Parameters of Pert Distribution by Using Method of Moments." International Journal for Research in Applied Science and Engineering Technology 9, no. 9 (September 30, 2021): 1621–29. http://dx.doi.org/10.22214/ijraset.2021.38239.

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Abstract: The method of moments has been widely used for estimating the parameters of a distribution. Usually lower order moments are wont to find the parameter estimates as they're known to possess less sampling variability. The method of moments may be a technique for estimating the parameters of a statistical model. It works by finding values of the parameters that end in a match between the sample moments and therefore the population moments (as implied by the model). the Method of moment Estimator is used to find out Estimates the parameters of PERT Distribution. We also compare equispaced and unequispaced Optimally Constructed Grouped data by the method of an Asymptotically Relative Efficiency. We also computed Average Estimate (AE), Variance (VAR), Standard Deviation (STD), Mean Absolute Deviation (MAD), Mean Square Error (MSE), Simulated Error (SE) and Relative Absolute Bias (RAB) for both the parameters under grouped sample supported 1000 simulations to assess the performance of the estimators. Keywords: Method of Moments, PERT Distribution, equispaced and unequipped Optimal Grouped sample

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3

Andrews, Donald W. K. "Consistent Moment Selection Procedures for Generalized Method of Moments Estimation." Econometrica 67, no. 3 (May 1999): 543–63. http://dx.doi.org/10.1111/1468-0262.00036.

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4

Mat Jan, Nur Amalina, Ani Shabri, and Ruhaidah Samsudin. "Handling non-stationary flood frequency analysis using TL-moments approach for estimation parameter." Journal of Water and Climate Change 11, no. 4 (August 16, 2019): 966–79. http://dx.doi.org/10.2166/wcc.2019.055.

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Abstract Non-stationary flood frequency analysis (NFFA) plays an important role in addressing the issue of the stationary assumption (independent and identically distributed flood series) that is no longer valid in infrastructure-designed methods. This confirms the necessity of developing new statistical models in order to identify the change of probability functions over time and obtain a consistent flood estimation method in NFFA. The method of Trimmed L-moments (TL-moments) with time covariate is confronted with the L-moment method for the stationary and non-stationary generalized extreme value (GEV) models. The aims of the study are to investigate the behavior of the proposed TL-moments method in the presence of NFFA and applying the method along with GEV distribution. Comparisons of the methods are made by Monte Carlo simulations and bootstrap-based method. The simulation study showed the better performance of most levels of TL-moments method, which is TL(η,0), (η = 2, 3, 4) than the L-moment method for all models (GEV1, GEV2, and GEV3). The TL-moment method provides more efficient quantile estimates than other methods in flood quantiles estimated at higher return periods. Thus, the TL-moments method can produce better estimation results since the L-moment eliminates lowest value and gives more weight to the largest value which provides important information.

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5

Nghiem, Linh H., Michael C. Byrd, and Cornelis J. Potgieter. "Estimation in linear errors-in-variables models with unknown error distribution." Biometrika 107, no. 4 (May 21, 2020): 841–56. http://dx.doi.org/10.1093/biomet/asaa025.

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Summary Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known or estimable from replicate data. A generalized method of moments approach can be used to estimate model parameters in the absence of knowledge of the error distributions, but it requires the existence of a large number of model moments. In this paper, parameter estimation based on the phase function, a normalized version of the characteristic function, is considered. This approach requires the model covariates to have asymmetric distributions, while the error distributions are symmetric. Parameters are estimated by minimizing a distance function between the empirical phase functions of the noisy covariates and the outcome variable. No knowledge of the measurement error distribution is needed to calculate this estimator. Both asymptotic and finite-sample properties of the estimator are studied. The connection between the phase function approach and method of moments is also discussed. The estimation of standard errors is considered and a modified bootstrap algorithm for fast computation is proposed. The newly proposed estimator is competitive with the generalized method of moments, despite making fewer model assumptions about the moment structure of the measurement error. Finally, the proposed method is applied to a real dataset containing measurements of air pollution levels.

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6

Frazier, David, and Eric Renault. "Indirect Inference: Which Moments to Match?" Econometrics 7, no. 1 (March 19, 2019): 14. http://dx.doi.org/10.3390/econometrics7010014.

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The standard approach to indirect inference estimation considers that the auxiliary parameters, which carry the identifying information about the structural parameters of interest, are obtained from some recently identified vector of estimating equations. In contrast to this standard interpretation, we demonstrate that the case of overidentified auxiliary parameters is both possible, and, indeed, more commonly encountered than one may initially realize. We then revisit the “moment matching” and “parameter matching” versions of indirect inference in this context and devise efficient estimation strategies in this more general framework. Perhaps surprisingly, we demonstrate that if one were to consider the naive choice of an efficient Generalized Method of Moments (GMM)-based estimator for the auxiliary parameters, the resulting indirect inference estimators would be inefficient. In this general context, we demonstrate that efficient indirect inference estimation actually requires a two-step estimation procedure, whereby the goal of the first step is to obtain an efficient version of the auxiliary model. These two-step estimators are presented both within the context of moment matching and parameter matching.

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7

Chatelain, Jean-Bernard. "Improving consistent moment selection procedures for generalized method of moments estimation." Economics Letters 95, no. 3 (June 2007): 380–85. http://dx.doi.org/10.1016/j.econlet.2006.11.011.

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8

Wilhelm, Daniel. "OPTIMAL BANDWIDTH SELECTION FOR ROBUST GENERALIZED METHOD OF MOMENTS ESTIMATION." Econometric Theory 31, no. 5 (October 2, 2014): 1054–77. http://dx.doi.org/10.1017/s026646661400067x.

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A two-step generalized method of moments estimation procedure can be made robust to heteroskedasticity and autocorrelation in the data by using a nonparametric estimator of the optimal weighting matrix. This paper addresses the issue of choosing the corresponding smoothing parameter (or bandwidth) so that the resulting point estimate is optimal in a certain sense. We derive an asymptotically optimal bandwidth that minimizes a higher-order approximation to the asymptotic mean-squared error of the estimator of interest. We show that the optimal bandwidth is of the same order as the one minimizing the mean-squared error of the nonparametric plugin estimator, but the constants of proportionality are significantly different. Finally, we develop a data-driven bandwidth selection rule and show, in a simulation experiment, that it may substantially reduce the estimator’s mean-squared error relative to existing bandwidth choices, especially when the number of moment conditions is large.

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9

Hu, Yi, Xiaohua Xia, Ying Deng, and Dongmei Guo. "Higher Order Mean Squared Error of Generalized Method of Moments Estimators for Nonlinear Models." Discrete Dynamics in Nature and Society 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/324904.

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Generalized method of moments (GMM) has been widely applied for estimation of nonlinear models in economics and finance. Although generalized method of moments has good asymptotic properties under fairly moderate regularity conditions, its finite sample performance is not very well. In order to improve the finite sample performance of generalized method of moments estimators, this paper studies higher-order mean squared error of two-step efficient generalized method of moments estimators for nonlinear models. Specially, we consider a general nonlinear regression model with endogeneity and derive the higher-order asymptotic mean square error for two-step efficient generalized method of moments estimator for this model using iterative techniques and higher-order asymptotic theories. Our theoretical results allow the number of moments to grow with sample size, and are suitable for general moment restriction models, which contains conditional moment restriction models as special cases. The higher-order mean square error can be used to compare different estimators and to construct the selection criteria for improving estimator’s finite sample performance.

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10

Wooldridge, Jeffrey M. "Applications of Generalized Method of Moments Estimation." Journal of Economic Perspectives 15, no. 4 (November 1, 2001): 87–100. http://dx.doi.org/10.1257/jep.15.4.87.

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I describe how the method of moments approach to estimation, including the more recent generalized method of moments (GMM) theory, can be applied to problems using cross section, time series, and panel data. Method of moments estimators can be attractive because in many circumstances they are robust to failures of auxiliary distributional assumptions that are not needed to identify key parameters. I conclude that while sophisticated GMM estimators are indispensable for complicated estimation problems, it seems unlikely that GMM will provide convincing improvements over ordinary least squares and two-stage least squares--by far the most common method of moments estimators used in econometrics--in settings faced most often by empirical researchers.

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11

Pedersen, Rasmus Søndergaard. "TARGETING ESTIMATION OF CCC-GARCH MODELS WITH INFINITE FOURTH MOMENTS." Econometric Theory 32, no. 2 (September 7, 2015): 498–531. http://dx.doi.org/10.1017/s0266466615000316.

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As an alternative to quasi-maximum likelihood, targeting estimation is a much applied estimation method for univariate and multivariate GARCH models. In terms of variance targeting estimation, recent research has pointed out that at least finite fourth moments of the data generating process is required, if one wants to perform inference in GARCH models by relying on asymptotic normality of the estimator. Such moment conditions may not be satisfied in practice for financial returns, highlighting a potential drawback of variance targeting estimation. In this paper, we consider the large-sample properties of the variance targeting estimator for the multivariate extended constant conditional correlation GARCH model when the distribution of the data generating process has infinite fourth moments. Using nonstandard limit theory, we derive new results for the estimator stating that, under suitable conditions, its limiting distribution is multivariate stable. The rate of consistency of the estimator is slower than$\sqrt T$and depends on the tail shape of the data generating process. A simulation study illustrates the derived properties of the targeting estimator.

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12

Dey, Sanku, Enayetur Raheem, and Saikat Mukherjee. "Statistical properties and different methods of estimation of transmuted Rayleigh distribution." Revista Colombiana de Estadística 40, no. 1 (January 16, 2017): 165–203. http://dx.doi.org/10.15446/rce.v40n1.56153.

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This article addresses the various properties and different methods of estimation of the unknown parameters of the Transmuted Rayleigh (TR) distribution from the frequentist point of view. Although, our main focus is on estimation from frequentist point of view, yet, various mathematical and statistical properties of the TR distribution (such as quantiles, moments, moment generating function, conditional moments, hazard rate, mean residual lifetime, mean past lifetime, mean deviation about mean and median, the stochastic ordering, various entropies, stress-strength parameter and order statistics) are derived. We briefly describe different frequentist methods of estimation approaches, namely, maximum likelihood estimators, moments estimators, L-moment estimators, percentile based estimators, least squares estimators, method of maximum product of spacings, method of Cram\'er-von-Mises, methods of Anderson-Darling and right-tail Anderson-Darling and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of two real data sets which is further illustrated by obtaining bias and standard error of the estimates and the bootstrap percentile confidence intervals using bootstrap resampling.

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13

Hall, Alastair R., Atsushi Inoue, Kalidas Jana, and Changmock Shin. "Information in generalized method of moments estimation and entropy-based moment selection." Journal of Econometrics 138, no. 2 (June 2007): 488–512. http://dx.doi.org/10.1016/j.jeconom.2006.05.006.

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14

Louzada, Francisco, Pedro L. Ramos, and Gleici S. C. Perdoná. "Different Estimation Procedures for the Parameters of the Extended Exponential Geometric Distribution for Medical Data." Computational and Mathematical Methods in Medicine 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/8727951.

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We have considered different estimation procedures for the unknown parameters of the extended exponential geometric distribution. We introduce different types of estimators such as the maximum likelihood, method of moments, modified moments,L-moments, ordinary and weighted least squares, percentile, maximum product of spacings, and minimum distance estimators. The different estimators are compared by using extensive numerical simulations. We discovered that the maximum product of spacings estimator has the smallest mean square errors and mean relative estimates, nearest to one, for both parameters, proving to be the most efficient method compared to other methods. Combining these results with the good properties of the method such as consistency, asymptotic efficiency, normality, and invariance we conclude that the maximum product of spacings estimator is the best one for estimating the parameters of the extended exponential geometric distribution in comparison with its competitors. For the sake of illustration, we apply our proposed methodology in two important data sets, demonstrating that the EEG distribution is a simple alternative to be used for lifetime data.

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15

Newey, Whitney K., and Kenneth D. West. "Hypothesis Testing with Efficient Method of Moments Estimation." International Economic Review 28, no. 3 (October 1987): 777. http://dx.doi.org/10.2307/2526578.

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16

Kanaya, Nobuhiro, Youji Iiguni, and Hajime Maeda. "2-D DOA estimation method using Zernike moments." Signal Processing 82, no. 3 (March 2002): 521–26. http://dx.doi.org/10.1016/s0165-1684(01)00204-3.

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17

Peter Boswijk, H., and Roy van der Weide. "Method of moments estimation of GO-GARCH models." Journal of Econometrics 163, no. 1 (July 2011): 118–26. http://dx.doi.org/10.1016/j.jeconom.2010.11.011.

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18

Purczyński, Jan. "Simplified Method of GED Distribution Parameters Estimation." Folia Oeconomica Stetinensia 10, no. 2 (January 1, 2012): 35–49. http://dx.doi.org/10.2478/v10031-011-0043-9.

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Simplified Method of GED Distribution Parameters EstimationIn this paper a simplified method of estimating GED distribution parameters has been proposed. The method uses first, second and 0.5-th order absolute moments. Unlike in maximum likelihood method, which involves solving a set of equations including special mathematical functions, the solution is given in the form of a simple relation. Application of three different approximations of Euler's gamma function value results in three different sets of results for which the χ2test is conducted. As a final solution (estimation of distribution parameters) the set is chosen which yields the smallest value of the χ2test statistic. The method proposed in this paper yields the χ2test statistic value which does not exceed the value of statistic for a distribution with parameters obtained with the maximum likelihood method.

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19

Pawlak, Mirosław, Gurmukh Singh Panesar, and Marcin Korytkowski. "A Novel Method for Invariant Image Reconstruction." Journal of Artificial Intelligence and Soft Computing Research 11, no. 1 (January 1, 2021): 69–80. http://dx.doi.org/10.2478/jaiscr-2021-0005.

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AbstractIn this paper we propose a novel method for invariant image reconstruction with the properly selected degree of symmetry. We make use of Zernike radial moments to represent an image due to their invariance properties to isometry transformations and the ability to uniquely represent the salient features of the image. The regularized ridge regression estimation strategy under symmetry constraints for estimating Zernike moments is proposed. This extended regularization problem allows us to enforces the bilateral symmetry in the reconstructed object. This is achieved by the proper choice of two regularization parameters controlling the level of reconstruction accuracy and the acceptable degree of symmetry. As a byproduct of our studies we propose an algorithm for estimating an angle of the symmetry axis which in turn is used to determine the possible asymmetry present in the image. The proposed image recovery under the symmetry constraints model is tested in a number of experiments involving image reconstruction and symmetry estimation.

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20

Spikin, Stuart A. "Estimation of earthquake source parameters by the inversion of waveform data: Global seismicity, 1981-1983." Bulletin of the Seismological Society of America 76, no. 6 (December 1, 1986): 1515–41. http://dx.doi.org/10.1785/bssa0760061515.

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Abstract A waveform inversion algorithm, based on optimal filter theory, has been applied to the P waves from 260 of the largest earthquakes occurring during the years 1981 through 1983. Estimates of average focal depth, scalar moment, and deviatoric source mechanism have been obtained. For all except the largest events (M0 > 1027 dyne-cm), the scalar moments obtained in this study are close to, but somewhat larger than, the Harvard centroid-moment tensor (CMT) scalar moments. The CMT estimates of scalar moment are probably biased to low values due to the way unmodeled lateral heterogeneity affects the fitting procedure. For the largest events, however, source complexity can bias the scalar moments determined in this study to lower values, and the CMT scalar moments are probably more accurate. The moment tensor, CMT, and U.S. Geological Survey first-motion source mechanisms have been objectively compared by computing the locations of the vector representations of the mechanisms on the unit sphere. We find that the similarities and differences between these mechanisms can be related to the uncertainties inherent in each method for certain types of earthquakes: (1) lack of constraint on one of the nodal planes for dip-slip type mechanisms from first-motion analysis; (2) lack of resolution of the moment tensor elements defining the dip-slip component of faulting for shallow-focus earthquakes in the CMT method; and (3) lack of resolution of the moment tensor elements defining the strike-slip component of faulting in the P-wave inversion method used here. Thus, on the average, the first-motion and CMT methods yield the more reliable mechanisms for strike-slip-type earthquakes, and the method used in this study gives a more reliable result for shallow-focus earthquakes with dip-slip-type mechanisms. Finally, both of the moment tensor methods should yield reliable solutions for intermediate- and deep-focus earthquakes.

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Alshkaki, Rafid. "A Generalized Modification of the Kumaraswamy Distribution for Modeling and Analyzing Real-Life Data." Statistics, Optimization & Information Computing 8, no. 2 (May 28, 2020): 521–48. http://dx.doi.org/10.19139/soic-2310-5070-869.

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In this paper, a generalized modification of the Kumaraswamy distribution is proposed, and its distributional and characterizing properties are studied. This distribution is closed under scaling and exponentiation, and has some well-known distributions as special cases, such as the generalized uniform, triangular, beta, power function, Minimax, and some other Kumaraswamy related distributions. Moment generating function, Lorenz and Bonferroni curves, with its moments consisting of the mean, variance, moments about the origin, harmonic, incomplete, probability weighted, L, and trimmed L moments, are derived. The maximum likelihood estimation method is used for estimating its parameters and applied to six different simulated data sets of this distribution, in order to check the performance of the estimation method through the estimated parameters mean squares errors computed from the different simulated sample sizes. Finally, four real-life data sets are used to illustrate the usefulness and the flexibility of this distribution in application to real-life data.

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22

Johnson, Roger W., and Donna V. Kliche. "Large Sample Comparison of Parameter Estimates in Gamma Raindrop Distributions." Atmosphere 11, no. 4 (March 29, 2020): 333. http://dx.doi.org/10.3390/atmos11040333.

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Raindrop size distributions have been characterized through the gamma family. Over the years, quite a few estimates of these gamma parameters have been proposed. The natural question for the practitioner, then, is what estimation procedure should be used. We provide guidance in answering this question when a large sample size (>2000 drops) of accurately measured drops is available. Seven estimation procedures from the literature: five method of moments procedures, maximum likelihood, and a pseudo maximum likelihood procedure, were examined. We show that the two maximum likelihood procedures provide the best precision (lowest variance) in estimating the gamma parameters. Method of moments procedures involving higher-order moments, on the other hand, give rise to poor precision (high variance) in estimating these parameters. A technique called the delta method assisted in our comparison of these various estimation procedures.

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23

Lynch, Anthony W., and Jessica A. Wachter. "Using Samples of Unequal Length in Generalized Method of Moments Estimation." Journal of Financial and Quantitative Analysis 48, no. 1 (February 2013): 277–307. http://dx.doi.org/10.1017/s0022109013000070.

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AbstractThis paper describes estimation methods, based on the generalized method of moments (GMM), applicable in settings where time series have different starting or ending dates. We introduce two estimators that are more efficient asymptotically than standard GMM. We apply these to estimating predictive regressions in international data and show that the use of the full sample affects inference for assets with data available over the full period as well as for assets with data available for a subset of the period. Monte Carlo experiments demonstrate that reductions hold for small-sample standard errors as well as asymptotic ones.

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24

Huang, Mei Ling, and Xiang Raney-Yan. "A Method for Confidence Intervals of High Quantiles." Entropy 23, no. 1 (January 4, 2021): 70. http://dx.doi.org/10.3390/e23010070.

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The high quantile estimation of heavy tailed distributions has many important applications. There are theoretical difficulties in studying heavy tailed distributions since they often have infinite moments. There are also bias issues with the existing methods of confidence intervals (CIs) of high quantiles. This paper proposes a new estimator for high quantiles based on the geometric mean. The new estimator has good asymptotic properties as well as it provides a computational algorithm for estimating confidence intervals of high quantiles. The new estimator avoids difficulties, improves efficiency and reduces bias. Comparisons of efficiencies and biases of the new estimator relative to existing estimators are studied. The theoretical are confirmed through Monte Carlo simulations. Finally, the applications on two real-world examples are provided.

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Pérez-Sánchez, Belén, Martín González, Carmen Perea, and Jose J. López-Espín. "A New Computational Method for Estimating Simultaneous Equations Models Using Entropy as a Parameter Criteria." Mathematics 9, no. 7 (March 24, 2021): 700. http://dx.doi.org/10.3390/math9070700.

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Simultaneous Equations Models (SEM) is a statistical technique widely used in economic science to model the simultaneity relationship between variables. In the past years, this technique has also been used in other fields such as psychology or medicine. Thus, the development of new estimating methods is an important line of research. In fact, if we want to apply the SEM to medical problems with the main goal being to obtain the best approximation between the parameters of model and their estimations. This paper shows a computational study between different methods for estimating simultaneous equations models as well as a new method which allows the estimation of those parameters based on the optimization of the Bayesian Method of Moments and minimizing the Akaike Information Criteria. In addition, an entropy measure has been calculated as a parameter criteria to compare the estimation methods studied. The comparison between those methods is performed through an experimental study using randomly generated models. The experimental study compares the estimations obtained by the different methods as well as the efficiency when comparing solutions by Akaike Information Criteria and Entropy Measure. The study shows that the proposed estimation method offered better approximations and the entropy measured results more efficiently than the rest.

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VENEZIANO, DANIELE, and PIERLUIGI FURCOLO. "A MODIFIED DOUBLE TRACE MOMENT METHOD OF MULTIFRACTAL ANALYSIS." Fractals 07, no. 02 (June 1999): 181–95. http://dx.doi.org/10.1142/s0218348x99000207.

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The Double Trace Moment method for the estimation of parameters of universal multifractal measures is revisited. It is found that the method applies strictly to bare measures but is approximate for dressed measures, which are the only observable ones. The approximation stems from the fact that the double dressed moments used by the method do not scale as required to produce unbiased estimates of the parameters. Modified moments are proposed, which correctly scale for both bare and dressed measures. The original and modified methods are compared theoretically and numerically. Conditions under which the original method gives accurate and heavily biased estimates are identified.

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Podesta, J. J., M. A. Forman, C. W. Smith, D. C. Elton, Y. Malécot, and Y. Gagne. "Accurate estimation of third-order moments from turbulence measurements." Nonlinear Processes in Geophysics 16, no. 1 (February 17, 2009): 99–110. http://dx.doi.org/10.5194/npg-16-99-2009.

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Abstract. Politano and Pouquet's law, a generalization of Kolmogorov's four-fifths law to incompressible MHD, makes it possible to measure the energy cascade rate in incompressible MHD turbulence by means of third-order moments. In hydrodynamics, accurate measurement of third-order moments requires large amounts of data because the probability distributions of velocity-differences are nearly symmetric and the third-order moments are relatively small. Measurements of the energy cascade rate in solar wind turbulence have recently been performed for the first time, but without careful consideration of the accuracy or statistical uncertainty of the required third-order moments. This paper investigates the statistical convergence of third-order moments as a function of the sample size N. It is shown that the accuracy of the third-moment <(δ v||)3> depends on the number of correlation lengths spanned by the data set and a method of estimating the statistical uncertainty of the third-moment is developed. The technique is illustrated using both wind tunnel data and solar wind data.

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Gallant, A. Ronald, and George Tauchen. "Which Moments to Match?" Econometric Theory 12, no. 4 (October 1996): 657–81. http://dx.doi.org/10.1017/s0266466600006976.

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We describe an intuitive, simple, and systematic approach to generating moment conditions for generalized method of moments (GMM) estimation of the parameters of a structural model. The idea is to use the score of a density that has an analytic expression to define the GMM criterion. The auxiliary model that generates the score should closely approximate the distribution' of the observed data but is not required to nest it. If the auxiliary model nests the structural model then the estimator is as efficient as maximum likelihood. The estimator is advantageous when expectations under a structural model can be computed by simulation, by quadrature, or by analytic expressions but the likelihood cannot be computed easily.

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RAGUPATHI, S., and R. A. KING. "USING MOMENTS FOR 3-D MOTION PARAMETER ESTIMATION: A PURE ROTATION CASE." Journal of Circuits, Systems and Computers 02, no. 04 (December 1992): 335–58. http://dx.doi.org/10.1142/s0218126692000210.

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Moment Invariants (MIs) are widely used for object recognition. Most of the moment based object recognition work reported is for 2-Dimensional (2-D) objects only. There have been considerable attempts made in extending the 2-D MIs to 3-D space. However, using moments for 3-D motion parameter estimation is relatively neglected. In this paper we present two iterative schemes for motion estimation of planar objects using moments as features. One, using the Levinberg-Marquardt method, performs better compared with the other. Only the pure rotational case is considered. By using moments, the correspondence problem is completely eliminated. We show from simulation experiments that this method is a feasible one and the error performance is reasonable. As motion of a planar patch is considered, the algorithm estimates both the rotational parameters and the planar coefficients.

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Seo, Myung Hwan, Sueyoul Kim, and Young-Joo Kim. "Estimation of dynamic panel threshold model using Stata." Stata Journal: Promoting communications on statistics and Stata 19, no. 3 (September 2019): 685–97. http://dx.doi.org/10.1177/1536867x19874243.

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In this article, we develop a command, xthenreg, that implements the first-differenced generalized method of moments estimation of the dynamic panel threshold model that Seo and Shin (2016, Journal of Econometrics 195: 169–186) proposed. Furthermore, we derive the asymptotic variance formula for a kink-constrained generalized method of moments estimator of the dynamic threshold model and provide an estimation algorithm. We also propose a fast bootstrap algorithm to implement the bootstrap for the linearity test. We illustrate the use of xthenreg through a Monte Carlo simulation and an economic application.

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Munkhammar, Joakim, Lars Mattsson, and Jesper Rydén. "Polynomial probability distribution estimation using the method of moments." PLOS ONE 12, no. 4 (April 10, 2017): e0174573. http://dx.doi.org/10.1371/journal.pone.0174573.

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32

Bouchereau, F., and D. Brady. "Method-of-moments parameter estimation for compound fading processes." IEEE Transactions on Communications 56, no. 2 (February 2008): 166–72. http://dx.doi.org/10.1109/tcomm.2008.050437.

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33

YANAGIMOTO, Takemi. "Estimation Based on Estimating Equations. From the Maximum Likelihood Method and the Method of Moments." Japanese journal of applied statistics 24, no. 1 (1995): 1–12. http://dx.doi.org/10.5023/jappstat.24.1.

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Naveed-Shahzad, Mirza, Zahid Asghar, Farrukh Shehzad, and Mubeen Shahzadi. "Parameter Estimation of Power Function Distribution with TL-moments." Revista Colombiana de Estadística 38, no. 2 (July 15, 2015): 321–34. http://dx.doi.org/10.15446/rce.v38n2.51663.

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Accurate estimation of parameters of a probability distribution is of immense importance in statistics. Biased and imprecise estimation of parameters can lead to erroneous results. Our focus is to estimate the parameter of Power function distribution accurately because this density is now widely used for modelling various types of data. In this study, L-moments, TL-moments, LL-moments and LH-moments of Power function distribution are derived. In addition, the coefficient of variation, skewness and kurtosis are obtained by method of moments, L-moments and TL-moments. Parameters of the density are estimated using linear moments and compared with method of moments and MLE on the basis of bias, root mean square error and coefficients through simulation study. L-moments proved to be superior for the parameter estimation and this conclusion is equally true for different parametric values and sample size.

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Abouammoh, Abdulrahman, and Mohamed Kayid. "A New Flexible Generalized Lindley Model: Properties, Estimation and Applications." Symmetry 12, no. 10 (October 14, 2020): 1678. http://dx.doi.org/10.3390/sym12101678.

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A new method for generalizing the Lindley distribution, by increasing the number of mixed models is presented formally. This generalized model, which is called the generalized Lindley of integer order, encompasses the exponential and the usual Lindley distributions as special cases when the order of the model is fixed to be one and two, respectively. The moments, the variance, the moment generating function, and the failure rate function of the initiated model are extracted. Estimation of the underlying parameters by the moment and the maximum likelihood methods are acquired. The maximum likelihood estimation for the right censored data has also been discussed. In a simulation running for various orders and censoring rates, efficiency of the maximum likelihood estimator has been explored. The introduced model has ultimately been fitted to two real data sets to emphasize its application.

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Liu, Bin, Cindy Long Yu, Michael Joseph Price, and Yan Jiang. "Generalized Method of Moments Estimators for Multiple Treatment Effects Using Observational Data from Complex Surveys." Journal of Official Statistics 34, no. 3 (September 1, 2018): 753–84. http://dx.doi.org/10.2478/jos-2018-0035.

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Abstract In this article, we consider a generalized method moments (GMM) estimator to estimate treatment effects defined through estimation equations using an observational data set from a complex survey. We demonstrate that the proposed estimator, which incorporates both sampling probabilities and semiparametrically estimated self-selection probabilities, gives consistent estimates of treatment effects. The asymptotic normality of the proposed estimator is established in the finite population framework, and its variance estimation is discussed. In simulations, we evaluate our proposed estimator and its variance estimator based on the asymptotic distribution. We also apply the method to estimate the effects of different choices of health insurance types on healthcare spending using data from the Chinese General Social Survey. The results from our simulations and the empirical study show that ignoring the sampling design weights might lead to misleading conclusions.

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Zhu, Zhengwei, Jianjiang Zhou, and Hongyu Chu. "Synthetic Aperture Radar Image Background Clutter Fitting Using SKS + MoM-BasedG0Distribution." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/864019.

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G0distribution can accurately model various background clutters in the single-look and multilook synthetic aperture radar (SAR) images and is one of the most important statistic models in the field of SAR image clutter modeling. However, the parameter estimation ofG0distribution is difficult, which greatly limits the application of the distribution. In order to solve the problem, a fast and accurateG0distribution parameter estimation method, which combines second-kind statistics (SKS) technique with Freitas’ method of moment (MoM), is proposed. First we deduce the first and second second-kind characteristic functions ofG0distribution based on Mellin transform, and then the logarithm moments and the logarithm cumulants corresponding to the above-mentioned characteristic functions are derived; finally combined with Freitas’ method of moment, a simple iterative equation which is used for estimating theG0distribution parameters is obtained. Experimental results show that the proposed method has fast estimation speed and high fitting precision for various measured SAR image clutters with different resolutions and different number of looks.

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Qian, Bo, Xiao Yu Zhang, and Shuang Sun. "A Parameters Estimation Method for FH Signal Based on SPWVD." Advanced Materials Research 912-914 (April 2014): 1112–15. http://dx.doi.org/10.4028/www.scientific.net/amr.912-914.1112.

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Based on analyzing the generation mechanism and characteristics of frequency hopping signal, a method for estimating the parameter of FH signal utilizing SPWVD is proposed. The hop dwell time is estimated by detected frequency transforming moments between conjoint hop in time and frequency array. Further, the hop rate, instantaneous frequency is estimated. The results of simulation show that the method can effectively estimate the parameter of FH signal, has better accuracy of parameter estimation and less amount of computation.

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Westgate, Philip M. "A readily available improvement over method of moments for intra-cluster correlation estimation in the context of cluster randomized trials and fitting a GEE–type marginal model for binary outcomes." Clinical Trials 16, no. 1 (October 8, 2018): 41–51. http://dx.doi.org/10.1177/1740774518803635.

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Background/aims Cluster randomized trials are popular in health-related research due to the need or desire to randomize clusters of subjects to different trial arms as opposed to randomizing each subject individually. As outcomes from subjects within the same cluster tend to be more alike than outcomes from subjects within other clusters, an exchangeable correlation arises that is measured via the intra-cluster correlation coefficient. Intra-cluster correlation coefficient estimation is especially important due to the increasing awareness of the need to publish such values from studies in order to help guide the design of future cluster randomized trials. Therefore, numerous methods have been proposed to accurately estimate the intra-cluster correlation coefficient, with much attention given to binary outcomes. As marginal models are often of interest, we focus on intra-cluster correlation coefficient estimation in the context of fitting such a model with binary outcomes using generalized estimating equations. Traditionally, intra-cluster correlation coefficient estimation with generalized estimating equations has been based on the method of moments, although such estimators can be negatively biased. Furthermore, alternative estimators that work well, such as the analysis of variance estimator, are not as readily applicable in the context of practical data analyses with generalized estimating equations. Therefore, in this article we assess, in terms of bias, the readily available residual pseudo-likelihood approach to intra-cluster correlation coefficient estimation with the GLIMMIX procedure of SAS (SAS Institute, Cary, NC). Furthermore, we study a possible corresponding approach to confidence interval construction for the intra-cluster correlation coefficient. Methods We utilize a simulation study and application example to assess bias in intra-cluster correlation coefficient estimates obtained from GLIMMIX using residual pseudo-likelihood. This estimator is contrasted with method of moments and analysis of variance estimators which are standards of comparison. The approach to confidence interval construction is assessed by examining coverage probabilities. Results Overall, the residual pseudo-likelihood estimator performs very well. It has considerably less bias than moment estimators, which are its competitor for general generalized estimating equation–based analyses, and therefore, it is a major improvement in practice. Furthermore, it works almost as well as analysis of variance estimators when they are applicable. Confidence intervals have near-nominal coverage when the intra-cluster correlation coefficient estimate has negligible bias. Conclusion Our results show that the residual pseudo-likelihood estimator is a good option for intra-cluster correlation coefficient estimation when conducting a generalized estimating equation–based analysis of binary outcome data arising from cluster randomized trials. The estimator is practical in that it is simply a result from fitting a marginal model with GLIMMIX, and a confidence interval can be easily obtained. An additional advantage is that, unlike most other options for performing generalized estimating equation–based analyses, GLIMMIX provides analysts the option to utilize small-sample adjustments that ensure valid inference.

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Erickson, Timothy, Robert Parham, and Toni M. Whited. "Fitting the Errors-in-variables Model Using High-order Cumulants and Moments." Stata Journal: Promoting communications on statistics and Stata 17, no. 1 (March 2017): 116–29. http://dx.doi.org/10.1177/1536867x1701700107.

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In this article, we consider a multiple mismeasured regressor errors-in-variables model. We present xtewreg, a command for using two-step generalized method of moments and minimum distance estimators that exploit overidentifying information contained in high-order cumulants or moments of the data. The command supports cumulant or moment estimation, internal support for the bootstrap with moment condition recentering, an arbitrary number of mismeasured regressors and perfectly measured regressors, and cumulants or moments up to an arbitrary degree. We also demonstrate how to use the estimators in the context of a corporate leverage regression.

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Arellano, Manuel. "Sargan's Intrumental Variables Estimation and the Generalized Method of Moments." Journal of Business & Economic Statistics 20, no. 4 (October 2002): 450–59. http://dx.doi.org/10.1198/073500102288618595.

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Yang, S., and J. K. Kim. "A note on multiple imputation for method of moments estimation." Biometrika 103, no. 1 (February 5, 2016): 244–51. http://dx.doi.org/10.1093/biomet/asv073.

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Rahman, Mezbahur, Dayeong An, and Mohammad Shaha Alam Patwary. "METHOD OF MOMENTS PARAMETER ESTIMATION FOR BETA INVERSE WEIBULL DISTRIBUTION." Far East Journal of Mathematical Sciences (FJMS) 97, no. 5 (June 20, 2015): 655–65. http://dx.doi.org/10.17654/fjmsjul2015_655_665.

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Kitamura, Yuichi, and Michael Stutzer. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation." Econometrica 65, no. 4 (July 1997): 861. http://dx.doi.org/10.2307/2171942.

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Munkhammar, Joakim, Lars Mattsson, and Jesper Rydén. "Correction: Polynomial probability distribution estimation using the method of moments." PLOS ONE 14, no. 7 (July 5, 2019): e0219530. http://dx.doi.org/10.1371/journal.pone.0219530.

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Wu, Yihong, and Pengkun Yang. "Optimal estimation of Gaussian mixtures via denoised method of moments." Annals of Statistics 48, no. 4 (August 2020): 1981–2007. http://dx.doi.org/10.1214/19-aos1873.

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Oh, Dong Hwan, and Andrew J. Patton. "Simulated Method of Moments Estimation for Copula-Based Multivariate Models." Journal of the American Statistical Association 108, no. 502 (June 2013): 689–700. http://dx.doi.org/10.1080/01621459.2013.785952.

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Anatolyev, Stanislav. "Method-of-moments estimation and choice of instruments: Numerical computations." Economics Letters 100, no. 2 (August 2008): 217–20. http://dx.doi.org/10.1016/j.econlet.2008.01.015.

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Park, Suk K., Sung K. Ahn, and Sinsup Cho. "Generalized method of moments estimation for cointegrated vector autoregressive models." Computational Statistics & Data Analysis 55, no. 9 (September 2011): 2605–18. http://dx.doi.org/10.1016/j.csda.2011.03.010.

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Parajuli, Ayush. "Evaluation of weibull parameter estimators for wind speed of Jumla, Nepal." Journal of Engineering Issues and Solutions 1, no. 1 (May 1, 2021): 1–7. http://dx.doi.org/10.3126/joeis.v1i1.36812.

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Weibull Probability Distribution Function (PDF) is widely used across world for estimation of wind power. Weibull function is a two parameter probability distribution function. The methods employed for the evaluation of these two parameters are critical for the efficient use of Weibull PDF. In the present study, three different Weibull PDF parameter estimators have been evaluated. For this purpose, the daily averaged wind speed data of Jumla Station, Nepal for period of 10 year (2004 – 2014: 2012 excluded) is studied. The parameter estimator evaluated in this study are Method of Moments (MoM), Least Square Error Method (LSEM) and Power Density Method (PDM). It has been found that Method of Moments (MoM) is the best estimator for evaluating Weibull Parameters.

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