On unbiased and improved loss estimation for the mean of a multivariate normal distribution with unknown variance

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	On unbiased and improved loss estimation for the mean of a multivariate normal distribution with unknown variance
	Wan, ATK ; Zou, GH
	2004-01-15
发表期刊	JOURNAL OF STATISTICAL PLANNING AND INFERENCE
ISSN	0378-3758
卷号	119 期号:1 页码:17-22
摘要	There is now a sizeable literature dealing with point estimation using Stein-type estimators. As discussed in Rukhin (In: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics, Vol. IV, Springer, New York, pp. 409-418), instances arise in practice in which an estimation rule is to be accompanied by an estimate of its loss, which is unobservable. In the context of estimating the mean vector of a multi-normal distribution assuming a known population variance, Johnstone (In: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics, Vol. IV, Springer, New York, pp, 361-379) derived an estimator that dominates the unbiased estimator of the quadratic loss incurred by the James-Stein estimator. By applying the Stein's lemma, this note generalizes Johnstone's (In: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics, Vol. IV, Springer, New York, pp. 361-379) analysis to the setting of the unknown population variance. Computational evidence is provided about the risk magnitude of loss estimators associated with the James-Stein point estimator and its positive-part version. (C) 2002 Elsevier B.V. All rights reserved.
关键词	James-Stein estimator positive-part rule risk quadratic loss
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000186911800002
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19763
专题	中国科学院数学与系统科学研究院
通讯作者	Wan, ATK
作者单位	1.City Univ Hong Kong, Dept Management Sci, Kowloon, Hong Kong, Peoples R China 2.Chinese Acad Sci, Inst Syst Sci, Beijing 100080, Peoples R China 3.Yale Univ, Dept Epidemiol & Publ Hlth, Div Biostat, New Haven, CT 06520 USA
推荐引用方式 GB/T 7714	Wan, ATK,Zou, GH. On unbiased and improved loss estimation for the mean of a multivariate normal distribution with unknown variance[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE,2004,119(1):17-22.
APA	Wan, ATK,&Zou, GH.(2004).On unbiased and improved loss estimation for the mean of a multivariate normal distribution with unknown variance.JOURNAL OF STATISTICAL PLANNING AND INFERENCE,119(1),17-22.
MLA	Wan, ATK,et al."On unbiased and improved loss estimation for the mean of a multivariate normal distribution with unknown variance".JOURNAL OF STATISTICAL PLANNING AND INFERENCE 119.1(2004):17-22.