The Annals of Statistics

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

L. R. Haff

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62C99: None of the above, but in this section

Keywords
Inverse covariance matrix Stokes' theorem integration by parts Stein-like estimators quadratic loss

Citation

Haff, L. R. Estimation of the Inverse Covariance Matrix: Random Mixtures of the Inverse Wishart Matrix and the Identity. Ann. Statist. 7 (1979), no. 6, 1264--1276. doi:10.1214/aos/1176344845. https://projecteuclid.org/euclid.aos/1176344845


Export citation

Corrections

  • See Correction: L. R. Haff. Corrections to "Estimation of the Inverse Covariance Matrix: Random Mixtures of the Inverse Wishart Matrix and the Identity". Ann. Statist., Volume 9, Number 5 (1981), 1132--1132.