ESTIMATING COVARIANCE MATRICES
成果类型：
Article
署名作者：
LOH, WL
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176347982
发表日期：
1991
页码：
283-296
关键词：
摘要：
Let S1 and S2 be two independent p x p Wishart matrices with S1 approximately W(p)(SIGMA-1, n1) and S2 approximately W(p)(SIGMA-2, n2). We wish to estimate (SIGMA-1, SIGMA-2) under the loss function L(SIGMA-1, SIGMA-2; SIGMA-1, SIGMA-2) = SIGMA-i{tr(SIGMA-i-1-SIGMA-i) - log\SIGMA-i-1-SIGMA-i\ - p}. Our approach is to first utilize the principle of invariance to narrow the class of estimators under consideration to the equivariant ones. The unbiased estimates of risk of these estimators are then computed and promising estimators are derived from them. A Monte Carlo study is also conducted to evaluate the risk performances of these estimators. The results of this paper extend those of Stein, Haff, Dey and Srinivasan from the one sample problem to the two sample one.