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.
Publié le : 1979-11-14
Classification:
Inverse covariance matrix,
Stokes' theorem,
integration by parts,
Stein-like estimators,
quadratic loss,
62F10,
62C99
@article{1176344845,
author = {Haff, L. R.},
title = {Estimation of the Inverse Covariance Matrix: Random Mixtures of the Inverse Wishart Matrix and the Identity},
journal = {Ann. Statist.},
volume = {7},
number = {1},
year = {1979},
pages = { 1264-1276},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344845}
}
Haff, L. R. Estimation of the Inverse Covariance Matrix: Random Mixtures of the Inverse Wishart Matrix and the Identity. Ann. Statist., Tome 7 (1979) no. 1, pp. 1264-1276. http://gdmltest.u-ga.fr/item/1176344845/