Improved nonnegative estimation of multivariate components of variance

• 成果类型: Article
• 署名作者: Srivastava, MS; Kubokawa, T
• 署名单位: University of Toronto; University of Tokyo
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 2008-2032
• 关键词: normal covariance-matrix; models

摘要

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.