The Annals of Statistics
- Ann. Statist.
- Volume 27, Number 6 (1999), 2008-2032.
Improved nonnegative estimation of multivariate components of variance
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.
Ann. Statist., Volume 27, Number 6 (1999), 2008-2032.
First available in Project Euclid: 4 April 2002
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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