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.
