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A Review on Empirical Likelihood Methods for Regression
, 2009
"... We provide a review on the empirical likelihood method for regression type inference problems. The regression models considered in this review include parametric, semiparametric and nonparametric models. Both missing data and censored data are accommodated. ..."
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We provide a review on the empirical likelihood method for regression type inference problems. The regression models considered in this review include parametric, semiparametric and nonparametric models. Both missing data and censored data are accommodated.
ASYMPTOTIC EQUIVALENCE OF EMPIRICAL LIKELIHOOD AND BAYESIAN MAP
, 908
"... In this paper we are interested in empirical likelihood (EL) as a method of estimation, and we address the following two problems: (1) selecting among various empirical discrepancies in an EL framework and (2) demonstrating that EL has a welldefined probabilistic interpretation that would justify i ..."
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In this paper we are interested in empirical likelihood (EL) as a method of estimation, and we address the following two problems: (1) selecting among various empirical discrepancies in an EL framework and (2) demonstrating that EL has a welldefined probabilistic interpretation that would justify its use in a Bayesian context. Using the large deviations approach, a Bayesian law of large numbers is developed that implies that EL and the Bayesian maximum a posteriori probability (MAP) estimators are consistent under misspecification and that EL can be viewed as an asymptotic form of MAP. Estimators based on other empirical discrepancies are, in general, inconsistent under misspecification. 1. Introduction. Owen’s empirical likelihood (EL) theorem ([30] and [31]) provides under traditional assumptions a basis for forming confidence regions for multivariate means and parameters in estimating equations. The basic EL idea is to proceed as if the sample X1,X2,...,Xn, drawn from an
Efficient parameter estimation in regression with missing responses
, 2012
"... Abstract: We discuss efficient estimation in regression models that are defined by a finitedimensional parametric constraint. This includes a variety of regression models, in particular the basic nonlinear regression model and quasilikelihood regression. We are interested in the case where respon ..."
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Abstract: We discuss efficient estimation in regression models that are defined by a finitedimensional parametric constraint. This includes a variety of regression models, in particular the basic nonlinear regression model and quasilikelihood regression. We are interested in the case where responses are missing at random. This is a popular research topic and various methods have been proposed in the literature. However, many of them are complicated and are not shown to be efficient. The method presented here is, in contrast, very simple we use an estimating equation that does not impute missing responses and we also prove that it is efficient if an appropriate weight matrix is selected. Finally, we show that this weight matrix can be replaced by a consistent estimator without losing the efficiency property.
Generalized Method of Moments Estimator Based On Semiparametric Quantile Regression
"... In this article, we consider an imputation method to handle missing response values based on semiparametric quantile regression estimation. In the proposed method, the missing response values are generated using the estimated conditional quantile regression function at given values of covariates. W ..."
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In this article, we consider an imputation method to handle missing response values based on semiparametric quantile regression estimation. In the proposed method, the missing response values are generated using the estimated conditional quantile regression function at given values of covariates. We adopt the generalized method of moments for estimation of parameters defined through a general estimation equation. We demonstrate that the proposed estimator, which combines both semiparametric quantile regression imputation and generalized method of moments, has competitive edge against some of the most widely used parametric and nonparametric imputation estimators. The consistency and the asymptotic normality of our estimator are established and variance estimation is provided. Results from a limited simulation study and an empirical study are presented to show the adequacy of the proposed method. Key Words: generalized method of moments, imputation, semiparametric quantile regression. 1
STATISTICAL EVALUATION OF CONTINUOUSSCALE DIAGNOSTIC TESTS WITH MISSING DATA
"... The receiver operating characteristic (ROC) curve methodology is the statistical methodology for assessment of the accuracy of diagnostics tests or biomarkers. Currently most widely used statistical methods for the inferences of ROC curves are completedata based parametric, semiparametric or nonp ..."
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The receiver operating characteristic (ROC) curve methodology is the statistical methodology for assessment of the accuracy of diagnostics tests or biomarkers. Currently most widely used statistical methods for the inferences of ROC curves are completedata based parametric, semiparametric or nonparametric methods. However, these methods cannot be used in diagnostic applications with missing data. In practical situations, missing diagnostic data occur more commonly due to various reasons such as medical tests being too expensive, too time consuming or too invasive. This dissertation aims to develop new nonparametric statistical methods for evaluating the accuracy of diagnostic tests or biomarkers in the presence of missing data. Specifically, novel nonparametric statistical methods will be developed with different types of missing data for (i) the inference of the area under the ROC curve (AUC, which is a summary index for the diagnostic accuracy of the test) and (ii) the joint inference of the sensitivity and the specificity of a continuousscale diagnostic test. In this dissertation, we will provide a general framework that combines the empirical likelihood and general estimation equations with nuisance parameters for the joint inferences of sensi
WITH MISSING DATA by
"... The receiver operating characteristic (ROC) curve methodology is the statistical methodology for assessment of the accuracy of diagnostics tests or biomarkers. Currently most widely used statistical methods for the inferences of ROC curves are completedata based parametric, semiparametric or nonp ..."
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The receiver operating characteristic (ROC) curve methodology is the statistical methodology for assessment of the accuracy of diagnostics tests or biomarkers. Currently most widely used statistical methods for the inferences of ROC curves are completedata based parametric, semiparametric or nonparametric methods. However, these methods cannot be used in diagnostic applications with missing data. In practical situations, missing diagnostic data occur more commonly due to various reasons such as medical tests being tooexpensive, too time consuming or too invasive. This dissertation aims to develop new nonparametric statistical methods for evaluating the accuracy of diagnostic tests or biomarkers in the presence of missing data. Specifically, novel nonparametric statistical methods will be developed with different types of missing data for (i) the inference of the area under the ROC curve (AUC, which is a summary index for the diagnostic accuracy of the test) and (ii) the joint inference of the sensitivity and the specificity of a continuousscale diagnostic test. In this dissertation, we will provide a general framework that combines the empirical likelihood and general estimation equations with nuisance parameters for the joint inferences of sensitivity