Improved nonnegative estimation of multivariate components of variance
The Annals of Statistics · 1999 · Volume 27 · Issue 6
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.
Keywords
62C12, 62C20, 62F30, 62H12, minimax and unbiased estimators, random effects model, restricted maximum likelihood estimator, Stein loss
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