#### Title

Linear empirical Bayes estimation in the case of the Wishart distribution

#### Keywords

empirical Bayes estimation; the Wishart distribution; COVARIANCE-MATRIX; MINIMAX ESTIMATORS; MOMENTS; Statistics & Probability

#### Abstract

We consider independent pairs (X-1, Sigma(1)), (X-2, Sigma(2)), ..., (X-n, Sigma(n)), where each Sigma(i) is distributed according to some unknown density function g(Sigma) and, given Sigma(i) = Sigma, X-i has a conditional density function q(x\Sigma) of the Wishart type. In each pair, the first component is observable but the second is not. After the (n + 1)-th observation Xn+1 is obtained, the objective is to estimate Sigma(n+1) corresponding to Xn+1. This estimator is called an empirical Bayes (EB) estimator of Sigma. We construct a linear EB estimator of Sigma and examine its precision.

#### Publication Title

Communications in Statistics-Theory and Methods

#### Volume

29

#### Issue/Number

8

#### Publication Date

1-1-2000

#### Document Type

Article

#### Language

English

#### First Page

1787

#### Last Page

1799

#### WOS Identifier

#### ISSN

0361-0926

#### Recommended Citation

Pensky, M., Kirtane, K. (2000). Linear empirical Bayes estimation in the case of the Wishart distribution. Communications in Statistics-Theory and Methods, 29(8). doi: 10.1080/03610920008832578

## Comments

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