The Annals of Statistics

Improved nonnegative estimation of multivariate components of variance

T. Kubokawa and M. S. Srivastava

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 27, Number 6 (1999), 2008-2032.

Dates
First available in Project Euclid: 4 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1017939248

Digital Object Identifier
doi:10.1214/aos/1017939248

Mathematical Reviews number (MathSciNet)
MR1765626

Zentralblatt MATH identifier
0961.62054

Subjects
Primary: 62H12: Estimation 62F30: Inference under constraints
Secondary: 62C12: Empirical decision procedures; empirical Bayes procedures 62C20: Minimax procedures

Keywords
Random effects model Stein loss minimax and unbiased estimators restricted maximum likelihood estimator

Citation

Srivastava, M. S.; Kubokawa, T. Improved nonnegative estimation of multivariate components of variance. Ann. Statist. 27 (1999), no. 6, 2008--2032. doi:10.1214/aos/1017939248. https://projecteuclid.org/euclid.aos/1017939248


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