A general approach to nonparametric empirical bayes estimation

    Authors

    M. Pensky

    Comments

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    Abbreviated Journal Title

    Statistics

    Keywords

    empirical Bay estimation; posterior quadratic risk; convergence rate; reliability characteristics; RATES; MODELS; Statistics & Probability

    Abstract

    Let (X(1), theta(1)), (X(2), theta(2)), ..., (X(N), theta(N)), (X(N+1), theta(N+1)) be independent random vectors with each theta(i) distributed according to some unknown prior density g. Given theta(i), let X(i) have the conditional density q(i)(x/theta(i)), 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(theta(N+1)) of theta(N+1). A general technique for construction of empirical Bayes estimators of b(theta(N+1)) is proposed and their convergence rates are examined. The special case, when the conditional densities q(i)(x/theta), i=1, ..., N+1, are identical, is also discussed. The theory is used to estimate of some reliability characteristics of nuclear power plant equipment.

    Journal Title

    Statistics

    Volume

    29

    Issue/Number

    1

    Publication Date

    1-1-1997

    Document Type

    Article

    Language

    English

    First Page

    61

    Last Page

    80

    WOS Identifier

    WOS:A1997WR59900003

    ISSN

    0233-1888

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