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On robust empirical bayes analysis of means and variances from stratified samples
Authors:Ram C Tiwari  Parthasarathi Lahiri
Institution:1. Department of Mathematics , University of North Carolina , Charlotte, NC, 28223;2. Department of Mathematics and Statistics , University of Nebraska-Lincoln , Lincoln, NE, 68588-0323
Abstract:Ghosh and Lahiri (1987a,b) considered simultaneous estimation of several strata means and variances where each stratum contains a finite number of elements, under the assumption that the posterior expectation of any stratum mean is a linear function of the sample observations - the so called“posterior linearity” property. In this paper we extend their result by retaining the “posterior linearity“ property of each stratum mean but allowing the superpopulation model whose mean as well as the variance-covariance structure changes from stratum to stratum. The performance of the proposed empirical Bayes estimators are found to be satisfactory both in terms of “asymptotic optimality” (Robbins (1955)) and “relative savings loss” (Efron and Morris (1973)).
Keywords:estimation  Bayes  Empirical Bayes  Bayes risk  relative savings loss  asymptotic optimality  stratified samples  means  variances  superpopulations
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