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December, 1987 Best Equivariant Estimators of a Cholesky Decomposition
Morris L. Eaton, Ingram Olkin
Ann. Statist. 15(4): 1639-1650 (December, 1987). DOI: 10.1214/aos/1176350615

Abstract

Every positive definite matrix $\Sigma$ has a unique Cholesky decomposition $\Sigma = \theta\theta'$, where $\theta$ is lower triangular with positive diagonal elements. Suppose that $S$ has a Wishart distribution with mean $n\Sigma$ and that $S$ has the Cholesky decomposition $S = XX'$. We show, for a variety of loss functions, that $XD$, where $D$ is diagonal, is a best equivariant estimator of $\theta$. Explicit expressions for $D$ are provided.

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Morris L. Eaton. Ingram Olkin. "Best Equivariant Estimators of a Cholesky Decomposition." Ann. Statist. 15 (4) 1639 - 1650, December, 1987. https://doi.org/10.1214/aos/1176350615

Information

Published: December, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0629.62057
MathSciNet: MR913579
Digital Object Identifier: 10.1214/aos/1176350615

Subjects:
Primary: 62H10
Secondary: 15A23, 15A52

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 4 • December, 1987
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