## The Annals of Statistics

### Best Equivariant Estimators of a Cholesky Decomposition

#### 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.

#### Article information

Source
Ann. Statist., Volume 15, Number 4 (1987), 1639-1650.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350615

Digital Object Identifier
doi:10.1214/aos/1176350615

Mathematical Reviews number (MathSciNet)
MR913579

Zentralblatt MATH identifier
0629.62057

JSTOR