The problem of finding classes of estimators which dominate the usual estimator $X$ of the mean vector $\mu$ of a $p$-variate normal distribution $(p \geq 3)$ under general quadratic loss is analytically difficult in cases where the covariance matrix is unknown. Estimators of $\mu$ in this case depend upon $X$ and an independent Wishart matrix $W$. In the present paper, integration-by-parts methods for both the multivariate normal and Wishart distributions are combined to yield unbiased estimates of risk difference (versus $X$) for certain classes of estimators, defined indirectly through a "seed" function $h(X, W)$. An application of this technique produces a new class of minimax estimators of $\mu$.
Publié le : 1986-12-14
Classification:
Integration-by-parts identities,
unbiased estimates of risk difference,
Wishart distribution,
62C20,
62F11,
62H99,
62J07
@article{1176350184,
author = {Gleser, Leon Jay},
title = {Minimax Estimators of a Normal Mean Vector for Arbitrary Quadratic Loss and Unknown Covariance Matrix},
journal = {Ann. Statist.},
volume = {14},
number = {2},
year = {1986},
pages = { 1625-1633},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350184}
}
Gleser, Leon Jay. Minimax Estimators of a Normal Mean Vector for Arbitrary Quadratic Loss and Unknown Covariance Matrix. Ann. Statist., Tome 14 (1986) no. 2, pp. 1625-1633. http://gdmltest.u-ga.fr/item/1176350184/