Comparison of Normal Variance Estimators in Terms of Pitman Nearness Criterion

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Title:	Comparison of Normal Variance Estimators in Terms of Pitman Nearness Criterion
Authors:	林志娟;張慶暉
Contributors:	淡江大學統計學系
Keywords:	損失函數;風險函數;非中央卡方分配;Loss Function;Risk Function;Non-Central Chi-Square Distribution;Affine Equivariance
Date:	2002-03
Issue Date:	2014-02-12 13:57:20 (UTC+8)
Abstract:	For estimating a normal variance under squared error loss function it is well known that the best affine (location and scale) equivariant estimator, which is better than the maximum likelihood estimator as well as the unbiased estimator, is also inadmissible. The improved estimators, e.g. Stein type, Brown type and Brewster-Zidek type, are all scale equivariant but not location invariant. Lately a good amount of research has been done to compare the improved estimators in terms of risk, but very little attention had been paid to compare these estimators in terms of Pitman nearness criterion. In this paper we have undertaken a comprehensive study to compare various variance estimators in terms of Pitman nearness criterion, which has long been over due, and have made some interesting observations in the process.
Relation:	e世紀的挑戰：國際學術研討會管理組論文集=Proceedings of E-Era Challenge International Academic Conference，頁545-562
Appears in Collections:	[Graduate Institute & Department of Statistics] Proceeding

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