The Annals of Statistics

Improved nonnegative estimation of multivariate components of variance

T. Kubokawa and M. S. Srivastava

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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

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

First available in Project Euclid: 4 April 2002

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Zentralblatt MATH identifier

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

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


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.

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