In this paper,we consider a multivariate one-way random effect model
with equal replications. We propose nonnegative definite estimators for
“between” and “within” components of variance.
Under the Stein loss function, it is shown that the proposed estimators of the
“within” component dominate the best unbiased estimator.
Restricted maximum likelihood, truncated and order-preserving minimax
estimators are also proposed. A Monte Carlo simulation is carried out to choose
among these estimators. For estimating the “between” component,
we consider the Stein loss function for jointly estimating the two positive
definite matrices (“within” and “within” plus
“between”) and obtain estimators for the “between”
component dominating the best unbiased estimator. Other estimators as
considered for “within” are also proposed. A Monte Carlo
simulation is carried out to choose among these estimators.
Publié le : 1999-12-14
Classification:
Random effects model,
Stein loss,
minimax and unbiased estimators,
restricted maximum likelihood estimator,
62H12,
62F30,
62C12,
62C20
@article{1017939248,
author = {Srivastava, M. S. and Kubokawa, T.},
title = {Improved nonnegative estimation of multivariate components of
variance},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 2008-2032},
language = {en},
url = {http://dml.mathdoc.fr/item/1017939248}
}
Srivastava, M. S.; Kubokawa, T. Improved nonnegative estimation of multivariate components of
variance. Ann. Statist., Tome 27 (1999) no. 4, pp. 2008-2032. http://gdmltest.u-ga.fr/item/1017939248/