## The Annals of Statistics

### Estimation of the Inverse Covariance Matrix: Random Mixtures of the Inverse Wishart Matrix and the Identity

L. R. Haff

#### Abstract

Let $S_{p \times p}$ have a nonsingular Wishart distribution with unknown matrix $\Sigma$ and $k$ degrees of freedom. For two different loss functions, estimators of $\Sigma^{-1}$ are given which dominate the obvious estimators $aS^{-1}, 0 < a \leqslant k - p - 1$. Our class of estimators $\mathscr{C}$ includes random mixtures of $S^{-1}$ and $I$. A subclass $\mathscr{C}_0 \subset \mathscr{C}$ was given by Haff. Here, we show that any member of $\mathscr{C}_0$ is dominated in $\mathscr{C}$. Some troublesome aspects of the estimation problem are discussed, and the theory is supplemented by simulation results.

#### Article information

Source
Ann. Statist., Volume 7, Number 6 (1979), 1264-1276.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176344845

Digital Object Identifier
doi:10.1214/aos/1176344845

Mathematical Reviews number (MathSciNet)
MR550149

Zentralblatt MATH identifier
0436.62046

JSTOR