James-Stein estimation problem for a multivariate normal random matrix and an improved estimator

doi:10.1016/j.laa.2017.06.032

CORC > 上海财经大学 > 上海财经大学

	James-Stein estimation problem for a multivariate normal random matrix and an improved estimator
	Liu, Xiaoqian 1; Liu, Liangyuan 2; Hu, Jianhua 2
刊名	LINEAR ALGEBRA AND ITS APPLICATIONS
	2017-11
卷号	532 页码:231-256
关键词	Admissibility James-Stein estimator James-Stein estimation problem Lost function Minimaxity Multivariate linear model Shrinkage estimator
ISSN号	0024-3795
DOI	10.1016/j.laa.2017.06.032
英文摘要	In this paper, we provide the proof of nonexistence of the James-Stein estimator in the whole parameter space for normal random matrices, equivalently, for multivariate linear regression models, which solves the open problem raised by S.F. Arnold [1]. By introducing the concepts of left and right James-Stein estimators, we obtain the left James-Stein estimator of mean matrix and show that the left James-Stein estimator has minimaxity and optimality in terms of the Efron-Morris type modification. We construct a new minimax combination estimator with lower risk by absorbing the advantages of the left James-Stein estimator and the existing modified Stein estimator. Risk comparisons through finite sample simulation studies illustrate that the proposed combination estimator has a better performance, under the mean-squared error or l(2) risk, compared with all existing estimators. (C) 2017 Elsevier Inc. All rights reserved.
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER SCIENCE INC
WOS记录号	WOS:000411297500015
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/869]
专题	上海财经大学
通讯作者	Hu, Jianhua
作者单位	1.Shanghai Int Studies Univ, Sch Econ & Finance, Shanghai 200083, Peoples R China; 2.Shanghai Univ Finance & Econ, Sch Stat & Management, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Liu, Xiaoqian,Liu, Liangyuan,Hu, Jianhua. James-Stein estimation problem for a multivariate normal random matrix and an improved estimator[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2017,532:231-256.
APA	Liu, Xiaoqian,Liu, Liangyuan,&Hu, Jianhua.(2017).James-Stein estimation problem for a multivariate normal random matrix and an improved estimator.LINEAR ALGEBRA AND ITS APPLICATIONS,532,231-256.
MLA	Liu, Xiaoqian,et al."James-Stein estimation problem for a multivariate normal random matrix and an improved estimator".LINEAR ALGEBRA AND ITS APPLICATIONS 532(2017):231-256.