Journal articles: 'Inverse estimator'

1

Karniel, Amir, Ron Meir, and Gideon F. Inbar. "Best estimated inverse versus inverse of the best estimator." Neural Networks 14, no. 9 (2001): 1153–59. http://dx.doi.org/10.1016/s0893-6080(01)00098-3.

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KUNDHI, GUBHINDER, and MARCEL VOIA. "Bootstrap bias correction for average treatment effects with inverse propensity weights." Journal of Statistical Research 52, no. 2 (2019): 187–200. http://dx.doi.org/10.47302/jsr.2018520205.

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The estimated average treatment effect in observational studies is biased if the assumptions of ignorability and overlap are not satisfied. To deal with this potential problem when propensity score weights are used in the estimation of the treatment effects, in this paper we propose a bootstrap bias correction estimator for the average treatment effect (ATE) obtained with the inverse propensity score (BBC-IPS) estimator. We show in simulations that the BBC-IPC performs well when we have misspecifications of the propensity score (PS) due to: omitted variables (ignorability property may not be satisfied), overlap (imbalances in distribution between treatment and control groups) and confounding effects between observables and unobservables (endogeneity). Further refinements in bias reductions of the ATE estimates in smaller samples are attained by iterating the BBC-IPS estimator.

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Balzer, Laura, Jennifer Ahern, Sandro Galea, and Mark van der Laan. "Estimating Effects with Rare Outcomes and High Dimensional Covariates: Knowledge is Power." Epidemiologic Methods 5, no. 1 (2016): 1–18. http://dx.doi.org/10.1515/em-2014-0020.

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AbstractMany of the secondary outcomes in observational studies and randomized trials are rare. Methods for estimating causal effects and associations with rare outcomes, however, are limited, and this represents a missed opportunity for investigation. In this article, we construct a new targeted minimum loss-based estimator (TMLE) for the effect or association of an exposure on a rare outcome. We focus on the causal risk difference and statistical models incorporating bounds on the conditional mean of the outcome, given the exposure and measured confounders. By construction, the proposed estimator constrains the predicted outcomes to respect this model knowledge. Theoretically, this bounding provides stability and power to estimate the exposure effect. In finite sample simulations, the proposed estimator performed as well, if not better, than alternative estimators, including a propensity score matching estimator, inverse probability of treatment weighted (IPTW) estimator, augmented-IPTW and the standard TMLE algorithm. The new estimator yielded consistent estimates if either the conditional mean outcome or the propensity score was consistently estimated. As a substitution estimator, TMLE guaranteed the point estimates were within the parameter range. We applied the estimator to investigate the association between permissive neighborhood drunkenness norms and alcohol use disorder. Our results highlight the potential for double robust, semiparametric efficient estimation with rare events and high dimensional covariates.

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Tan, Z. "Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data." Biometrika 107, no. 1 (2019): 137–58. http://dx.doi.org/10.1093/biomet/asz059.

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Summary Propensity scores are widely used with inverse probability weighting to estimate treatment effects in observational studies. We study calibrated estimation as an alternative to maximum likelihood estimation for fitting logistic propensity score models. We show that, with possible model misspecification, minimizing the expected calibration loss underlying the calibrated estimators involves reducing both the expected likelihood loss and a measure of relative errors between the limiting and true propensity scores, which governs the mean squared errors of inverse probability weighted estimators. Furthermore, we derive a regularized calibrated estimator by minimizing the calibration loss with a lasso penalty. We develop a Fisher scoring descent algorithm for computing the proposed estimator and provide a high-dimensional analysis of the resulting inverse probability weighted estimators, leveraging the control of relative errors of propensity scores for calibrated estimation. We present a simulation study and an empirical application to demonstrate the advantages of the proposed methods over maximum likelihood and its regularization. The methods are implemented in the R package RCAL.

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Lendle, Samuel David, Bruce Fireman, and Mark J. van der Laan. "Balancing Score Adjusted Targeted Minimum Loss-based Estimation." Journal of Causal Inference 3, no. 2 (2015): 139–55. http://dx.doi.org/10.1515/jci-2012-0012.

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AbstractAdjusting for a balancing score is sufficient for bias reduction when estimating causal effects including the average treatment effect and effect among the treated. Estimators that adjust for the propensity score in a nonparametric way, such as matching on an estimate of the propensity score, can be consistent when the estimated propensity score is not consistent for the true propensity score but converges to some other balancing score. We call this property the balancing score property, and discuss a class of estimators that have this property. We introduce a targeted minimum loss-based estimator (TMLE) for a treatment-specific mean with the balancing score property that is additionally locally efficient and doubly robust. We investigate the new estimator’s performance relative to other estimators, including another TMLE, a propensity score matching estimator, an inverse probability of treatment weighted estimator, and a regression-based estimator in simulation studies.

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Glynn, Adam N., and Kevin M. Quinn. "An Introduction to the Augmented Inverse Propensity Weighted Estimator." Political Analysis 18, no. 1 (2010): 36–56. http://dx.doi.org/10.1093/pan/mpp036.

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In this paper, we discuss an estimator for average treatment effects (ATEs) known as the augmented inverse propensity weighted (AIPW) estimator. This estimator has attractive theoretical properties and only requires practitioners to do two things they are already comfortable with: (1) specify a binary regression model for the propensity score, and (2) specify a regression model for the outcome variable. Perhaps the most interesting property of this estimator is its so-called “double robustness.” Put simply, the estimator remains consistent for the ATE if either the propensity score model or the outcome regression is misspecified but the other is properly specified. After explaining the AIPW estimator, we conduct a Monte Carlo experiment that compares the finite sample performance of the AIPW estimator to three common competitors: a regression estimator, an inverse propensity weighted (IPW) estimator, and a propensity score matching estimator. The Monte Carlo results show that the AIPW estimator has comparable or lower mean square error than the competing estimators when the propensity score and outcome models are both properly specified and, when one of the models is misspecified, the AIPW estimator is superior.

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Ni, Liqiang, and R. Dennis Cook. "A robust inverse regression estimator." Statistics & Probability Letters 77, no. 3 (2007): 343–49. http://dx.doi.org/10.1016/j.spl.2006.07.018.

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Mao, Huzhang, Liang Li, and Tom Greene. "Propensity score weighting analysis and treatment effect discovery." Statistical Methods in Medical Research 28, no. 8 (2018): 2439–54. http://dx.doi.org/10.1177/0962280218781171.

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Inverse probability weighting can be used to estimate the average treatment effect in propensity score analysis. When there is lack of overlap in the propensity score distributions between the treatment groups under comparison, some weights may be excessively large, causing numerical instability and bias in point and variance estimation. We study a class of modified inverse probability weighting estimators that can be used to avoid this problem. These weights cause the estimand to deviate from the average treatment effect. We provide some justification for this deviation from the perspective of treatment effect discovery. We show that when lack of overlap occurs, the modified weights can achieve substantial gains in statistical power compared with inverse probability weighting and other propensity score methods. We develop analytical variance estimates that properly adjust for the sampling variability of the estimated propensity scores, and augment the modified inverse probability weighting estimator with outcome models for improved efficiency, a property that resembles double robustness. Results from extensive simulations and a real data application support our conclusions. The proposed methodology is implemented in R package PSW.

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Moradi, Mohammad, Mohammad Salehi, Jennifer Ann Brown, and Naser Karimi. "Regression estimator under inverse sampling to estimate arsenic contamination." Environmetrics 22, no. 7 (2011): 894–900. http://dx.doi.org/10.1002/env.1116.

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Xiao, Min, Ting Chen, Kunpeng Huang, and Ruixing Ming. "Optimal Estimation for Power of Variance with Application to Gene-Set Testing." Journal of Systems Science and Information 8, no. 6 (2020): 549–64. http://dx.doi.org/10.21078/jssi-2020-549-16.

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Abstract Detecting differential expression of genes in genom research (e.g., 2019-nCoV) is not uncommon, due to the cost only small sample is employed to estimate a large number of variances (or their inverse) of variables simultaneously. However, the commonly used approaches perform unreliable. Borrowing information across different variables or priori information of variables, shrinkage estimation approaches are proposed and some optimal shrinkage estimators are obtained in the sense of asymptotic. In this paper, we focus on the setting of small sample and a likelihood-unbiased estimator for power of variances is given under the assumption that the variances are chi-squared distribution. Simulation reports show that the likelihood-unbiased estimators for variances and their inverse perform very well. In addition, application comparison and real data analysis indicate that the proposed estimator also works well.

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GAO, XIAOTIAN, XINXIN DONG, CHAERYON KANG KANG, and ABDUS S. WAHED. "Inference on mean quality-adjusted lifetime using joint models for continuous quality of life process and time to event." Journal of Statistical Research 53, no. 2 (2020): 165–89. http://dx.doi.org/10.47302/jsr.2019530205.

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The estimated average treatment effect in observational studies is biased if the assumptions of ignorability and overlap are not satisﬁed. To deal with this potential problem when propensity score weights are used in the estimation of the treatment effects, in this paper we propose a bootstrap bias correction estimator for the average treatment effect (ATE) obtained with the inverse propensity score (BBC-IPS) estimator. We show in simulations that the BBC-IPC performs well when we have misspeciﬁcations of the propensity score (PS) due to: omitted variables (ignorability property may not be satisﬁed), overlap (imbalances in distribution between treatment and control groups) and confounding effects between observables and unobservables (endogeneity). Further reﬁnements in bias reductions of the ATE estimates in smaller samples are attained by iterating the BBC-IPS estimator.

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Díaz, Iván, and Mark J. van der Laan. "Targeted Data Adaptive Estimation of the Causal Dose–Response Curve." Journal of Causal Inference 1, no. 2 (2013): 171–92. http://dx.doi.org/10.1515/jci-2012-0005.

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AbstractEstimation of the causal dose–response curve is an old problem in statistics. In a non-parametric model, if the treatment is continuous, the dose–response curve is not a pathwise differentiable parameter, and no -consistent estimator is available. However, the risk of a candidate algorithm for estimation of the dose–response curve is a pathwise differentiable parameter, whose consistent and efficient estimation is possible. In this work, we review the cross-validated augmented inverse probability of treatment weighted estimator (CV A-IPTW) of the risk and present a cross-validated targeted minimum loss–based estimator (CV-TMLE) counterpart. These estimators are proven consistent and efficient under certain consistency and regularity conditions on the initial estimators of the outcome and treatment mechanism. We also present a methodology that uses these estimated risks to select among a library of candidate algorithms. These selectors are proven optimal in the sense that they are asymptotically equivalent to the oracle selector under certain consistency conditions on the estimators of the treatment and outcome mechanisms. Because the CV-TMLE is a substitution estimator, it is more robust than the CV-AIPTW against empirical violations of the positivity assumption. This and other small sample size differences between the CV-TMLE and the CV-A-IPTW are explored in a simulation study.

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13

Shao, Jun, and Lei Wang. "Semiparametric inverse propensity weighting for nonignorable missing data." Biometrika 103, no. 1 (2016): 175–87. http://dx.doi.org/10.1093/biomet/asv071.

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Abstract To estimate unknown population parameters based on data having nonignorable missing values with a semiparametric exponential tilting propensity, Kim & Yu (2011) assumed that the tilting parameter is known or can be estimated from external data, in order to avoid the identifiability issue. To remove this serious limitation on the methodology, we use an instrument, i.e., a covariate related to the study variable but unrelated to the missing data propensity, to construct some estimating equations. Because these estimating equations are semiparametric, we profile the nonparametric component using a kernel-type estimator and then estimate the tilting parameter based on the profiled estimating equations and the generalized method of moments. Once the tilting parameter is estimated, so is the propensity, and then other population parameters can be estimated using the inverse propensity weighting approach. Consistency and asymptotic normality of the proposed estimators are established. The finite-sample performance of the estimators is studied through simulation, and a real-data example is also presented.

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Florens, Jean-Pierre, and Anna Simoni. "REGULARIZING PRIORS FOR LINEAR INVERSE PROBLEMS." Econometric Theory 32, no. 1 (2014): 71–121. http://dx.doi.org/10.1017/s0266466614000796.

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This paper proposes a new Bayesian approach for estimating, nonparametrically, functional parameters in econometric models that are characterized as the solution of a linear inverse problem. By using a Gaussian process prior we propose the posterior mean as an estimator and prove frequentist consistency of the posterior distribution. The latter provides the frequentist validation of our Bayesian procedure. We show that the minimax rate of contraction of the posterior distribution can be obtained provided that either the regularity of the prior matches the regularity of the true parameter or the prior is scaled at an appropriate rate. The scaling parameter of the prior distribution plays the role of a regularization parameter. We propose a new data-driven method for optimally selecting in practice this regularization parameter. We also provide sufficient conditions such that the posterior mean, in a conjugate-Gaussian setting, is equal to a Tikhonov-type estimator in a frequentist setting. Under these conditions our data-driven method is valid for selecting the regularization parameter of the Tikhonov estimator as well. Finally, we apply our general methodology to two leading examples in econometrics: instrumental regression and functional regression estimation.

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Et al., Khaleel. "Estimating the Reliability Function of (2+1) Cascade Model." Baghdad Science Journal 16, no. 2 (2019): 0395. http://dx.doi.org/10.21123/bsj.16.2.0395.

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This paper discusses reliability R of the (2+1) Cascade model of inverse Weibull distribution. Reliability is to be found when strength-stress distributed is inverse Weibull random variables with unknown scale parameter and known shape parameter. Six estimation methods (Maximum likelihood, Moment, Least Square, Weighted Least Square, Regression and Percentile) are used to estimate reliability. There is a comparison between six different estimation methods by the simulation study by MATLAB 2016, using two statistical criteria Mean square error and Mean Absolute Percentage Error, where it is found that best estimator between the six estimators is Maximum likelihood estimation method.

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Et al., Khaleel. "Estimating the Reliability Function of (2+1) Cascade Model." Baghdad Science Journal 16, no. 2 (2019): 0395. http://dx.doi.org/10.21123/bsj.2019.16.2.0395.

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This paper discusses reliability R of the (2+1) Cascade model of inverse Weibull distribution. Reliability is to be found when strength-stress distributed is inverse Weibull random variables with unknown scale parameter and known shape parameter. Six estimation methods (Maximum likelihood, Moment, Least Square, Weighted Least Square, Regression and Percentile) are used to estimate reliability. There is a comparison between six different estimation methods by the simulation study by MATLAB 2016, using two statistical criteria Mean square error and Mean Absolute Percentage Error, where it is found that best estimator between the six estimators is Maximum likelihood estimation method.

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Johannes, Jan, Sébastien Van Bellegem, and Anne Vanhems. "CONVERGENCE RATES FOR ILL-POSED INVERSE PROBLEMS WITH AN UNKNOWN OPERATOR." Econometric Theory 27, no. 3 (2010): 522–45. http://dx.doi.org/10.1017/s0266466610000393.

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This paper studies the estimation of a nonparametric functionϕfrom the inverse problemr=Tϕgiven estimates of the functionrand of the linear transformT. We show that rates of convergence of the estimator are driven by two types of assumptions expressed in a single Hilbert scale. The two assumptions quantify the prior regularity ofϕand the prior link existing betweenTand the Hilbert scale. The approach provides a unified framework that allows us to compare various sets of structural assumptions found in the econometric literature. Moreover, general upper bounds are also derived for the risk of the estimator of the structural functionϕas well as that of its derivatives. It is shown that the bounds cover and extend known results given in the literature. Two important applications are also studied. The first is the blind nonparametric deconvolution on the real line, and the second is the estimation of the derivatives of the nonparametric instrumental regression function via an iterative Tikhonov regularization scheme.

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Jacqmin-Gadda, Hélène, Paul Blanche, Emilie Chary, Célia Touraine, and Jean-François Dartigues. "Receiver operating characteristic curve estimation for time to event with semicompeting risks and interval censoring." Statistical Methods in Medical Research 25, no. 6 (2016): 2750–66. http://dx.doi.org/10.1177/0962280214531691.

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Semicompeting risks and interval censoring are frequent in medical studies, for instance when a disease may be diagnosed only at times of visit and disease onset is in competition with death. To evaluate the ability of markers to predict disease onset in this context, estimators of discrimination measures must account for these two issues. In recent years, methods for estimating the time-dependent receiver operating characteristic curve and the associated area under the ROC curve have been extended to account for right censored data and competing risks. In this paper, we show how an approximation allows to use the inverse probability of censoring weighting estimator for semicompeting events with interval censored data. Then, using an illness-death model, we propose two model-based estimators allowing to rigorously handle these issues. The first estimator is fully model based whereas the second one only uses the model to impute missing observations due to censoring. A simulation study shows that the bias for inverse probability of censoring weighting remains modest and may be less than the one of the two parametric estimators when the model is misspecified. We finally recommend the nonparametric inverse probability of censoring weighting estimator as main analysis and the imputation estimator based on the illness-death model as sensitivity analysis.

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Zhang, Yichong, and Xin Zheng. "Quantile treatment effects and bootstrap inference under covariate‐adaptive randomization." Quantitative Economics 11, no. 3 (2020): 957–82. http://dx.doi.org/10.3982/qe1323.

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In this paper, we study the estimation and inference of the quantile treatment effect under covariate‐adaptive randomization. We propose two estimation methods: (1) the simple quantile regression and (2) the inverse propensity score weighted quantile regression. For the two estimators, we derive their asymptotic distributions uniformly over a compact set of quantile indexes, and show that, when the treatment assignment rule does not achieve strong balance, the inverse propensity score weighted estimator has a smaller asymptotic variance than the simple quantile regression estimator. For the inference of method (1), we show that the Wald test using a weighted bootstrap standard error underrejects. But for method (2), its asymptotic size equals the nominal level. We also show that, for both methods, the asymptotic size of the Wald test using a covariate‐adaptive bootstrap standard error equals the nominal level. We illustrate the finite sample performance of the new estimation and inference methods using both simulated and real datasets.

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Gui, Wenhao, and Man Chen. "Parameter Estimation and Joint Confidence Regions for the Parameters of the Generalized Lindley Distribution." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/7946828.

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We deal with the problem of estimating the parameters of the generalized Lindley distribution. Besides the classical estimator, inverse moment and modified inverse estimators are proposed and their properties are investigated. A condition for the existence and uniqueness of the inverse moment and modified inverse estimators of the parameters is established. Monte Carlo simulations are conducted to compare the estimators’ performances. Two methods for constructing joint confidence regions for the two parameters are also proposed and their performances are discussed. A real example is presented to illustrate the proposed methods.

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Ding, Litao, and Peter Mathé. "Minimax Rates for Statistical Inverse Problems Under General Source Conditions." Computational Methods in Applied Mathematics 18, no. 4 (2018): 603–8. http://dx.doi.org/10.1515/cmam-2017-0055.

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AbstractWe describe the minimax reconstruction rates in linear ill-posed equations in Hilbert space when smoothness is given in terms of general source sets. The underlying fundamental result, the minimax rate on ellipsoids, is proved similarly to the seminal study by D. L. Donoho, R. C. Liu, and B. MacGibbon [4]. These authors highlighted the special role of the truncated series estimator, and for such estimators the risk can explicitly be given. We provide several examples, indicating results for statistical estimation in ill-posed problems in Hilbert space.

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Rao, G. Srinivasa, Sauda Mbwambo, and P. K. Josephat. "Estimation of Stress–Strength Reliability from Exponentiated Inverse Rayleigh Distribution." International Journal of Reliability, Quality and Safety Engineering 26, no. 01 (2019): 1950005. http://dx.doi.org/10.1142/s0218539319500050.

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This paper considers the estimation of stress–strength reliability when two independent exponential inverse Rayleigh distributions with different shape parameters and common scale parameter. The maximum likelihood estimator (MLE) of the reliability, its asymptotic distribution and asymptotic confidence intervals are constructed. Comparisons of the performance of the estimators are carried out using Monte Carlo simulations, the mean squared error (MSE), bias, average length and coverage probabilities. Finally, a demonstration is delivered on how the proposed reliability model may be applied in data analysis of the strength data for single carbon fibers test data.

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Zhou, Hui. "Data Processing and Technology Application in Bayes and Empirical Bayes Reliability Analysis of Parameter of Ailamujia Distribution." Advanced Materials Research 951 (May 2014): 249–52. http://dx.doi.org/10.4028/www.scientific.net/amr.951.249.

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The estimation of the parameter of the ЭРланга distribution is discussed based on complete samples. Bayes and empirical Bayesian estimators of the parameter of the ЭРланга distribution are obtained under squared error loss and LINEX loss by using conjugate prior inverse Gamma distribution. Finally, a Monte Carlo simulation example is used to compare the Bayes and empirical Bayes estimators with the maximum likelihood estimator.

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LEE, MING-HUI. "INVERSE DYNAMIC INPUT ESTIMATION OF A SEISMIC SOIL–STRUCTURE INTERACTION SYSTEM." International Journal of Applied Mechanics 06, no. 04 (2014): 1450040. http://dx.doi.org/10.1142/s1758825114500409.

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The innovative fuzzy weighting input estimation method is used to estimate the ground motion acceleration of a soil–structure interaction system in this study. The input estimation method is comprised of the Kalman filter without the input term and the fuzzy weighting recursive least square estimator. The recursive least squares estimator (RLSE) is weighted using the fuzzy weighting factor. The superior capabilities of this inverse method are demonstrated by solving the soil–structure interaction estimation problem. The precision of the proposed method is verified using the actual earthquake acceleration. The results show that this method has the advantages of stability and accuracy.

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Dong, Hao, and Daniel L. Millimet. "Propensity Score Weighting with Mismeasured Covariates: An Application to Two Financial Literacy Interventions." Journal of Risk and Financial Management 13, no. 11 (2020): 290. http://dx.doi.org/10.3390/jrfm13110290.

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Estimation of the causal effect of a binary treatment on outcomes often requires conditioning on covariates to address selection concerning observed variables. This is not straightforward when one or more of the covariates are measured with error. Here, we present a new semi-parametric estimator that addresses this issue. In particular, we focus on inverse propensity score weighting estimators when the propensity score is of an unknown functional form and some covariates are subject to classical measurement error. Our proposed solution involves deconvolution kernel estimators of the propensity score and the regression function weighted by a deconvolution kernel density estimator. Simulations and replication of a study examining the impact of two financial literacy interventions on the business practices of entrepreneurs show our estimator to be valuable to empirical researchers.

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Golan, Amos, and Henryk Gzyl. "An Entropic Estimator for Linear Inverse Problems." Entropy 14, no. 5 (2012): 892–923. http://dx.doi.org/10.3390/e14050892.

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van Opheusden, Bas, Luigi Acerbi, and Wei Ji Ma. "Unbiased and efficient log-likelihood estimation with inverse binomial sampling." PLOS Computational Biology 16, no. 12 (2020): e1008483. http://dx.doi.org/10.1371/journal.pcbi.1008483.

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The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter estimation and model evaluation. However, the log-likelihood of complex models in fields such as computational biology and neuroscience is often intractable to compute analytically or numerically. In those cases, researchers can often only estimate the log-likelihood by comparing observed data with synthetic observations generated by model simulations. Standard techniques to approximate the likelihood via simulation either use summary statistics of the data or are at risk of producing substantial biases in the estimate. Here, we explore another method, inverse binomial sampling (IBS), which can estimate the log-likelihood of an entire data set efficiently and without bias. For each observation, IBS draws samples from the simulator model until one matches the observation. The log-likelihood estimate is then a function of the number of samples drawn. The variance of this estimator is uniformly bounded, achieves the minimum variance for an unbiased estimator, and we can compute calibrated estimates of the variance. We provide theoretical arguments in favor of IBS and an empirical assessment of the method for maximum-likelihood estimation with simulation-based models. As case studies, we take three model-fitting problems of increasing complexity from computational and cognitive neuroscience. In all problems, IBS generally produces lower error in the estimated parameters and maximum log-likelihood values than alternative sampling methods with the same average number of samples. Our results demonstrate the potential of IBS as a practical, robust, and easy to implement method for log-likelihood evaluation when exact techniques are not available.

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Lee, Ming-Hui. "Estimation of structure system input force using the inverse fuzzy estimator." Structural Engineering and Mechanics 37, no. 4 (2011): 351–65. http://dx.doi.org/10.12989/sem.2011.37.4.351.

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Journal, Baghdad Science. "Bayes and Non-Bayes Estimation Methods for the Parameter of Maxwell-Boltzmann Distribution." Baghdad Science Journal 14, no. 4 (2017): 808–12. http://dx.doi.org/10.21123/bsj.14.4.808-812.

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In this paper, point estimation for parameter ? of Maxwell-Boltzmann distribution has been investigated by using simulation technique, to estimate the parameter by two sections methods; the first section includes Non-Bayesian estimation methods, such as (Maximum Likelihood estimator method, and Moment estimator method), while the second section includes standard Bayesian estimation method, using two different priors (Inverse Chi-Square and Jeffrey) such as (standard Bayes estimator, and Bayes estimator based on Jeffrey's prior). Comparisons among these methods were made by employing mean square error measure. Simulation technique for different sample sizes has been used to compare between these methods.

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Jacho-Chávez, David Tomás. "OPTIMAL BANDWIDTH CHOICE FOR ESTIMATION OF INVERSE CONDITIONAL–DENSITY–WEIGHTED EXPECTATIONS." Econometric Theory 26, no. 1 (2009): 94–118. http://dx.doi.org/10.1017/s0266466609090628.

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This paper characterizes the bandwidth value (h) that is optimal for estimating parameters of the form $\eta \, &#x003D; \,E\left[ {\omega /f_{V|U} \left({V|U} \right)} \right]$, where the conditional density of a scalar continuous random variable V, given a random vector U, $f_{V|U} $, is replaced by its kernel estimator. That is, the parameter η is the expectation of ω inversely weighted by $f_{V|U} $, and it is the building block of various semiparametric estimators already proposed in the literature such as Lewbel (1998), Lewbel (2000b), Honoré and Lewbel (2002), Khan and Lewbel (2007), and Lewbel (2007). The optimal bandwidth is derived by minimizing the leading terms of a second-order mean squared error expansion of an in-probability approximation of the resulting estimator with respect to h. The expansion also demonstrates that the bandwidth can be chosen on the basis of bias alone, and that a simple “plug-in” estimator for the optimal bandwidth can be constructed. Finally, the small sample performance of our proposed estimator of the optimal bandwidth is assessed by a Monte Carlo experiment.

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Riplinger, M., and M. Spiess. "Asymptotic Properties of the Approximate Inverse Estimator for Directional Distributions." Advances in Applied Probability 44, no. 04 (2012): 954–76. http://dx.doi.org/10.1017/s0001867800006005.

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For stationary fiber processes, the estimation of the directional distribution is an important task. We consider a stereological approach, assuming that the intersection points of the process with a finite number of test hyperplanes can be observed in a bounded window. The intensity of these intersection processes is proportional to the cosine transform of the directional distribution. We use the approximate inverse method to invert the cosine transform and analyze asymptotic properties of the estimator in growing windows for Poisson line processes. We show almost-sure convergence of the estimator and derive Berry–Esseen bounds, including formulae for the variance.

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Riplinger, M., and M. Spiess. "Asymptotic Properties of the Approximate Inverse Estimator for Directional Distributions." Advances in Applied Probability 44, no. 4 (2012): 954–76. http://dx.doi.org/10.1239/aap/1354716585.

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For stationary fiber processes, the estimation of the directional distribution is an important task. We consider a stereological approach, assuming that the intersection points of the process with a finite number of test hyperplanes can be observed in a bounded window. The intensity of these intersection processes is proportional to the cosine transform of the directional distribution. We use the approximate inverse method to invert the cosine transform and analyze asymptotic properties of the estimator in growing windows for Poisson line processes. We show almost-sure convergence of the estimator and derive Berry–Esseen bounds, including formulae for the variance.

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Ng, Set Foong, Pei Eng Ch’ng, Yee Ming Chew, and Kok Shien Ng. "Applying the Method of Lagrange Multipliers to Derive an Estimator for Unsampled Soil Properties." Scientific Research Journal 11, no. 1 (2014): 15. http://dx.doi.org/10.24191/srj.v11i1.5416.

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Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained.

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Ng, Set Foong, Pei Eng Ch’ng, Yee Ming Chew, and Kok Shien Ng. "Applying the Method of Lagrange Multipliers to Derive an Estimator for Unsampled Soil Properties." Scientific Research Journal 11, no. 1 (2014): 15. http://dx.doi.org/10.24191/srj.v11i1.9398.

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Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained.

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Hadad, Vitor, David A. Hirshberg, Ruohan Zhan, Stefan Wager, and Susan Athey. "Confidence intervals for policy evaluation in adaptive experiments." Proceedings of the National Academy of Sciences 118, no. 15 (2021): e2014602118. http://dx.doi.org/10.1073/pnas.2014602118.

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Adaptive experimental designs can dramatically improve efficiency in randomized trials. But with adaptively collected data, common estimators based on sample means and inverse propensity-weighted means can be biased or heavy-tailed. This poses statistical challenges, in particular when the experimenter would like to test hypotheses about parameters that were not targeted by the data-collection mechanism. In this paper, we present a class of test statistics that can handle these challenges. Our approach is to adaptively reweight the terms of an augmented inverse propensity-weighting estimator to control the contribution of each term to the estimator’s variance. This scheme reduces overall variance and yields an asymptotically normal test statistic. We validate the accuracy of the resulting estimates and their CIs in numerical experiments and show that our methods compare favorably to existing alternatives in terms of mean squared error, coverage, and CI size.

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Niilo-Rämä, Mikko, Salme Kärkkäinen, Dario Gasbarra, and Timo Lappalainen. "INCLUSION RATIO BASED ESTIMATOR FOR THE MEAN LENGTH OF THE BOOLEAN LINE SEGMENT MODEL WITH AN APPLICATION TO NANOCRYSTALLINE CELLULOSE." Image Analysis & Stereology 33, no. 2 (2014): 147. http://dx.doi.org/10.5566/ias.v33.p147-155.

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A novel estimator for estimating the mean length of fibres is proposed for censored data observed in square shaped windows. Instead of observing the fibre lengths, we observe the ratio between the intensity estimates of minus-sampling and plus-sampling. It is well-known that both intensity estimators are biased. In the current work, we derive the ratio of these biases as a function of the mean length assuming a Boolean line segment model with exponentially distributed lengths and uniformly distributed directions. Having the observed ratio of the intensity estimators, the inverse of the derived function is suggested as a new estimator for the mean length. For this estimator, an approximation of its variance is derived. The accuracies of the approximations are evaluated by means of simulation experiments. The novel method is compared to other methods and applied to real-world industrial data from nanocellulose crystalline.

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Kofman, W., and A. Silvent. "Adaptive Estimator of a Filter and Its Inverse." IEEE Transactions on Communications 33, no. 12 (1985): 1281–84. http://dx.doi.org/10.1109/tcom.1985.1096248.

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Li, Yunfan, Bruce A. Craig, and Anindya Bhadra. "The Graphical Horseshoe Estimator for Inverse Covariance Matrices." Journal of Computational and Graphical Statistics 28, no. 3 (2019): 747–57. http://dx.doi.org/10.1080/10618600.2019.1575744.

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Lim, Jong-Hwan, Heung-Su Kim, Jae-Hyuk Youn, et al. "Monopulse estimator using inverse function of MR curve." Electronics Letters 48, no. 23 (2012): 1497. http://dx.doi.org/10.1049/el.2012.0506.

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Mohsin, Muhammad, and Muhammad Qaiser Shahbaz. "Comparison of Negative Moment Estimator with Maximum Likelihood Estimator of Inverse Rayleigh Distribution." Pakistan Journal of Statistics and Operation Research 1, no. 1 (2005): 45. http://dx.doi.org/10.18187/pjsor.v1i1.115.

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Tan, Yaoyuan V., Carol A. C. Flannagan, and Michael R. Elliott. "“Robust-Squared” Imputation Models Using Bart." Journal of Survey Statistics and Methodology 7, no. 4 (2019): 465–97. http://dx.doi.org/10.1093/jssam/smz002.

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Abstract Examples of “doubly robust” estimators for missing data include augmented inverse probability weighting (AIPWT) and penalized splines of propensity prediction (PSPP). Doubly robust estimators have the property that, if either the response propensity or the mean is modeled correctly, a consistent estimator of the population mean is obtained. However, doubly robust estimators can perform poorly when modest misspecification is present in both models. Here we consider extensions of the AIPWT and PSPP that use Bayesian additive regression trees (BART) to provide highly robust propensity and mean model estimation. We term these “robust-squared” in the sense that the propensity score, the means, or both can be estimated with minimal model misspecification, and applied to the doubly robust estimator. We consider their behavior via simulations where propensities and/or mean models are misspecified. We apply our proposed method to impute missing instantaneous velocity (delta-v) values from the 2014 National Automotive Sampling System Crashworthiness Data System dataset and missing Blood Alcohol Concentration values from the 2015 Fatality Analysis Reporting System dataset. We found that BART, applied to PSPP and AIPWT, provides a more robust estimate compared with PSPP and AIPWT.

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Bellach, A., M. R. Kosorok, P. B. Gilbert, and J. P. Fine. "General regression model for the subdistribution of a competing risk under left-truncation and right-censoring." Biometrika 107, no. 4 (2020): 949–64. http://dx.doi.org/10.1093/biomet/asaa034.

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Summary Left-truncation poses extra challenges for the analysis of complex time-to-event data. We propose a general semiparametric regression model for left-truncated and right-censored competing risks data that is based on a novel weighted conditional likelihood function. Targeting the subdistribution hazard, our parameter estimates are directly interpretable with regard to the cumulative incidence function. We compare different weights from recent literature and develop a heuristic interpretation from a cure model perspective that is based on pseudo risk sets. Our approach accommodates external time-dependent covariate effects on the subdistribution hazard. We establish consistency and asymptotic normality of the estimators and propose a sandwich estimator of the variance. In comprehensive simulation studies we demonstrate solid performance of the proposed method. Comparing the sandwich estimator with the inverse Fisher information matrix, we observe a bias for the inverse Fisher information matrix and diminished coverage probabilities in settings with a higher percentage of left-truncation. To illustrate the practical utility of the proposed method, we study its application to a large HIV vaccine efficacy trial dataset.

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Krishna, Hare, Madhulika Dube, and Renu Garg. "Estimation of Stress Strength Reliability of Inverse Weibull Distribution under Progressive First Failure Censoring." Austrian Journal of Statistics 48, no. 1 (2018): 14–37. http://dx.doi.org/10.17713/ajs.v47i4.638.

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In this article, estimation of stress-strength reliability $\delta=P\left(Y<X\right)$ based on progressively first failure censored data from two independent inverse Weibull distributions with different shape and scale parameters is studied. Maximum likelihood estimator and asymptotic confidence interval of $\delta$ are obtained. Bayes estimator of $\delta$ under generalized entropy loss function using non-informative and gamma informative priors is derived. Also, highest posterior density credible interval of $\delta$ is constructed. Markov Chain Monte Carlo (MCMC) technique is used for Bayes computation. The performance of various estimation methods are compared by a Monte Carlo simulation study. Finally, a pair of real life data is analyzed to illustrate the proposed methods of estimation.

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del Álamo, Miguel, and Axel Munk. "Total variation multiscale estimators for linear inverse problems." Information and Inference: A Journal of the IMA 9, no. 4 (2020): 961–86. http://dx.doi.org/10.1093/imaiai/iaaa001.

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Abstract Even though the statistical theory of linear inverse problems is a well-studied topic, certain relevant cases remain open. Among these is the estimation of functions of bounded variation ($BV$), meaning $L^1$ functions on a $d$-dimensional domain whose weak first derivatives are finite Radon measures. The estimation of $BV$ functions is relevant in many applications, since it involves minimal smoothness assumptions and gives simplified, interpretable cartoonized reconstructions. In this paper, we propose a novel technique for estimating $BV$ functions in an inverse problem setting and provide theoretical guaranties by showing that the proposed estimator is minimax optimal up to logarithms with respect to the $L^q$-risk, for any $q\in [1,\infty )$. This is to the best of our knowledge the first convergence result for $BV$ functions in inverse problems in dimension $d\geq 2$, and it extends the results of Donoho (1995, Appl. Comput. Harmon. Anal., 2, 101–126) in $d=1$. Furthermore, our analysis unravels a novel regime for large $q$ in which the minimax rate is slower than $n^{-1/(d+2\beta +2)}$, where $\beta$ is the degree of ill-posedness: our analysis shows that this slower rate arises from the low smoothness of $BV$ functions. The proposed estimator combines variational regularization techniques with the wavelet-vaguelette decomposition of operators.

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Chu, Ba, and David T. Jacho-Chávez. "k-NEAREST NEIGHBOR ESTIMATION OF INVERSE-DENSITY-WEIGHTED EXPECTATIONS WITH DEPENDENT DATA." Econometric Theory 28, no. 4 (2012): 769–803. http://dx.doi.org/10.1017/s026646661100079x.

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This paper considers the problem of estimating expected values of functions that are inversely weighted by an unknown density using the k-nearest neighbor (k-NN) method. It establishes the $\root \of T $-consistency and the asymptotic normality of an estimator that allows for strictly stationary time-series data. The consistency of the Bartlett estimator of the derived asymptotic variance is also established. The proposed estimator is also shown to be asymptotically semiparametric efficient in the independent random sampling scheme. Monte Carlo experiments show that the proposed estimator performs well in finite sample applications.

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van Wieringen, Wessel N. "The Generalized Ridge Estimator of the Inverse Covariance Matrix." Journal of Computational and Graphical Statistics 28, no. 4 (2019): 932–42. http://dx.doi.org/10.1080/10618600.2019.1604374.

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Yahya Algamal, Zakariya. "Performance of ridge estimator in inverse Gaussian regression model." Communications in Statistics - Theory and Methods 48, no. 15 (2018): 3836–49. http://dx.doi.org/10.1080/03610926.2018.1481977.

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Khare, B. B., and B. K. Mishra. "An improved estimator for population proportion using inverse sampling." Microelectronics Reliability 34, no. 11 (1994): 1807–10. http://dx.doi.org/10.1016/0026-2714(94)90134-1.

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Akram, Muhammad Nauman, Muhammad Amin, and Muhammad Amanullah. "James Stein Estimator for the Inverse Gaussian Regression Model." Iranian Journal of Science and Technology, Transactions A: Science 45, no. 4 (2021): 1389–403. http://dx.doi.org/10.1007/s40995-021-01133-0.

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Kim, Kyung Youn, Bong Seok Kim, Ho Chan Kim, et al. "Inverse estimation of time-dependent boundary heat flux with an adaptive input estimator." International Communications in Heat and Mass Transfer 30, no. 4 (2003): 475–84. http://dx.doi.org/10.1016/s0735-1933(03)00076-9.

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Journal articles on the topic 'Inverse estimator'

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