ESTIMATING THE COMMON-MEAN OF 2 MULTIVARIATE NORMAL-DISTRIBUTIONS
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/1176347983
发表日期：
1991
页码：
297-313
关键词：
摘要：
Let X1, X2 be two p x 1 multivariate normal random vectors and S1, S2 be two p x p Wishart matrices, where X1 approximately N(p)(xi, SIGMA-1), X2 approximately N(p) (xi, SIGMA-2), S1 approximately W(p) (SIGMA-1, n) and S2 approximately W(p) (SIGMA-2, n). We further assume that X1, X2, S1, S2 are stochastically independent. We wish to estimate the common mean xi with respect to the loss function L = (xi - xi)'(SIGMA-1-1 + SIGMA-2-1)(xi - xi). By extending the methods of Stein and Haff, an alternative unbiased estimator to the usual generalized least squares estimator is obtained. However, the risk of this estimator is not available in closed form. A Monte Carlo swindle is used instead to evaluate its risk performance. The results indicate that the alternative estimator performs very favorably against the usual estimator.
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