#### Title

A general approach to nonparametric empirical bayes estimation

#### 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

#### ISSN

0233-1888

#### Recommended Citation

"A general approach to nonparametric empirical bayes estimation" (1997). *Faculty Bibliography 1990s*. 2050.

https://stars.library.ucf.edu/facultybib1990/2050

## Comments

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