Title

A general approach to nonparametric empirical Bayes estimation

Keywords

Convergence rate; Empirical Bay estimation; Posterior quadratic risk; Reliability characteristics

Abstract

Let (X1, θ1), (X2, θ2),⋯, (XN, 0N), (XN+1, 0N+1) be independent random vectors with each θi- distributed according to some unknown prior density g. Given θi, let Xi have the conditional density qi(x/θi), i = 1,⋯, N + 1. In each pair the first component is observable, but the second is not. The objective is to estimate a known function b(θN+1) of θN+1. A general technique for construction of empirical Bayes estimators of b(θN+1) is proposed and their convergence rates are examined. The special case, when the conditional densities qi(x/θ), i = 1,⋯, N + 1, are identical, is also discussed. The theory is used to estimate of some reliability characteristics of nuclear power plant equipment.

Publication Date

1-1-1997

Publication Title

Statistics

Volume

29

Issue

1

Number of Pages

61-80

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/02331889708802574

Socpus ID

0039319762 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0039319762

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