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December 1999 Improved nonnegative estimation of multivariate components of variance
T. Kubokawa, M. S. Srivastava
Ann. Statist. 27(6): 2008-2032 (December 1999). DOI: 10.1214/aos/1017939248

Abstract

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.

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T. Kubokawa. M. S. Srivastava. "Improved nonnegative estimation of multivariate components of variance." Ann. Statist. 27 (6) 2008 - 2032, December 1999. https://doi.org/10.1214/aos/1017939248

Information

Published: December 1999
First available in Project Euclid: 4 April 2002

zbMATH: 0961.62054
MathSciNet: MR1765626
Digital Object Identifier: 10.1214/aos/1017939248

Subjects:
Primary: 62F30, 62H12
Secondary: 62C12, 62C20

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 6 • December 1999
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