In the point and interval estimation of the variance of a normal distribution with an unknown mean, the best affine equivariant estimators are dominated by Stein's truncated and Brewster and Zidek's smooth procedures, which are separately derived. This paper gives a unified approach to this problem by using a simple definite integral and provides a class of improved procedures in both point and interval estimation of powers of the scale parameter of normal, lognormal, exponential and Pareto distributions. Finally, the same method is applied to the improvement on the James-Stein rule in the simultaneous estimation of a multinormal mean.
Publié le : 1994-03-14
Classification:
Point and interval estimation of variance,
best affine equivariant estimator,
inadmissibility,
Brewster-Zidek estimator,
normal,
exponential,
noncentral chi-square distribution,
simultaneous estimation of multinormal mean,
James-Stein rule,
62C99,
62F11,
62F25
@article{1176325369,
author = {Kubokawa, Tatsuya},
title = {A Unified Approach to Improving Equivariant Estimators},
journal = {Ann. Statist.},
volume = {22},
number = {1},
year = {1994},
pages = { 290-299},
language = {en},
url = {http://dml.mathdoc.fr/item/1176325369}
}
Kubokawa, Tatsuya. A Unified Approach to Improving Equivariant Estimators. Ann. Statist., Tome 22 (1994) no. 1, pp. 290-299. http://gdmltest.u-ga.fr/item/1176325369/