Inadmissibility and admissibility results for unbiased loss estimators based on gauss-markov estimators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Inadmissibility and admissibility results for unbiased loss estimators based on gauss-markov estimators

Authors:	Qiguang Wu

Institution:	(1) Institute of Systems Science, Academia Sinica, 100080 Beijing, China

Abstract:	LetY be distributed according to ann-variate normal distribution with a meanX and a nonsingular covariance matrix ² V, where bothX andV are known, R ^p is a parameter, > 0 is known or unknown. Denote $\hat \beta = (X'V^{ - 1} X)^ - X'V^{ - 1} Y$ and $S^2 = (Y - X\hat \beta )'V^{ - 1} (Y - X\hat \beta )$ . Assume thatF is linearly estimable. When is known, it is proved that the unbiased loss estimator ²tr(F(XV ^–1 X)^– F) of $(F\hat \beta - F\beta )'(F\hat \beta - F\beta )$ is admissible for rank (F)=k4 and inadmissible fork 5 with the squared error loss $a - (F\hat \beta - F\beta )'(F\hat \beta - F\beta )]^2$ . When is unknown and rank (X) <n, it is established that the loss estimatorcS ², wherec is any nonnegative constant, of $(F\hat \beta - F\beta )'(F\hat \beta - F\beta )$ is inadmissible and that the unbiased loss estimator tr(F(XV ^–1 X)^– F) of $\sigma ^{ - 2} (F\hat \beta - F\beta )'(F\hat \beta - F\beta )$ is admissible fork 4, and inadmissible fork 5 with squared error loss.This project is supported by the National Natural Science Foundation of China.

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