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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
Source PublicationJOURNAL OF STATISTICAL PLANNING AND INFERENCE
ISSN0378-3758
Volume119Issue:1Pages:17-22
AbstractThere 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.
KeywordJames-Stein estimator positive-part rule risk quadratic loss
Language英语
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000186911800002
PublisherELSEVIER SCIENCE BV
Citation statistics
Cited Times:6[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/19763
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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