ADMISSIBILITY AND Г-MINIMAXITY OF LOSSESTIMATORS IN MULTIVARIATE LINEAR MODEL  

作　　者：Kazuo Noda(Department of Mathematics, Science University of Tokyo, Tokyo, Japan 162)WU Qiguang(Institute of Systetns Science, Academia Sinica, Beijing 100080, China) 

出　　处：《Systems Science and Mathematical Sciences》1998年第1期69-81,共13页

摘　　要：Let an n x m matrix of observations, Y, have distribution N(XB, G V),where X, G > 0 and V > 0 are known n x p) n x n and m x m matrices respectively,B is an unknown P x m matrix of parameters. We consider the problem of estimatingthe loss L = (SXB - SXB)C(SXB - SXB)’, where S and C > 0 are known t x n andm x m matrices respectively B = (X’G-’X)-X’G-’y It is pr0ved that the uniformlyminimum risk unbiased estimator of L, L. = (trCV)SX(X’G-’X)-X’S’, is admissiblefor q = rankSX = 1 and m 4, or for q 2 and m 2 and inadmissible for m 5 witha matrix loss function. It is also shown that the above Lo is a r-minimax estimator 0f Lagainst a class of priors.Let an n x m matrix of observations, Y, have distribution N(XB, G V),where X, G > 0 and V > 0 are known n x p) n x n and m x m matrices respectively,B is an unknown P x m matrix of parameters. We consider the problem of estimatingthe loss L = (SXB - SXB)C(SXB - SXB)', where S and C > 0 are known t x n andm x m matrices respectively B = (X'G-'X)-X'G-'y It is pr0ved that the uniformlyminimum risk unbiased estimator of L, L. = (trCV)SX(X'G-'X)-X'S', is admissiblefor q = rankSX = 1 and m 4, or for q 2 and m 2 and inadmissible for m 5 witha matrix loss function. It is also shown that the above Lo is a r-minimax estimator 0f Lagainst a class of priors.

关 键 词：ADMISSIBLE LOSS ESTIMATOR r-minimax LOSS ESTIMATOR matrix LOSS function. 

分 类 号：O211[理学—概率论与数理统计]