The limiting bound of Efron's W-formula for hypothesis testing when a nuisance parameter is present only under the alternative

doi:10.1016/j.jspi.2009.12.021

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	The limiting bound of Efron's W-formula for hypothesis testing when a nuisance parameter is present only under the alternative
	Li, Qizhai1 ; Zheng, Gang 2; Liu, Aiyi 3; Xiong, Shifeng1 ; Li, Zhaohai 4,5; Yu, Kai 4
	2010-06-01
发表期刊	JOURNAL OF STATISTICAL PLANNING AND INFERENCE
ISSN	0378-3758
卷号	140 期号:6 页码:1610-1617
摘要	When testing a hypothesis with a nuisance parameter present only under the alternative, the maximum of a test statistic over the nuisance parameter space has been proposed. Different upper bounds for the one-sided tail probabilities of the maximum tests were provided. Davies (1977. Biometrika 64, 247-254) studied the problem when the parameter space is an interval, while Efron (1997. Biometrika 84, 143-157) considered the problem with some finite points of the parameter space and obtained a W-formula. We study the limiting bound of Efron's W-formula when the number of points in the parameter space goes to infinity. The conditions under which the limiting bound of the W-formula is identical to that of Davies are given. The results are also extended to two-sided tests. Examples are used to illustrate the conditions, including case-control genetic association studies. Efficient calculations of upper bounds for the tail probability with finite points in the parameter space are described. (C) 2009 Elsevier B.V. All rights reserved.
关键词	Hypothesis testing Limiting bound MAX Nuisance parameter Robustness W-formula
DOI	10.1016/j.jspi.2009.12.021
语种	英语
资助项目	National Institutes of Health ; National Young Science Foundation of China[10901155]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000275345500022
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/10423
专题	系统科学研究所
通讯作者	Li, Qizhai
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 2.NHLBI, Off Biostat Res, Div Prevent & Populat Sci, Bethesda, MD 20892 USA 3.NICHHD, Biometry & Math Stat Branch, Bethesda, MD 20892 USA 4.NCI, Div Canc Epidemiol & Genet, Bethesda, MD 20892 USA 5.George Washington Univ, Dept Stat, Washington, DC 20052 USA
推荐引用方式 GB/T 7714	Li, Qizhai,Zheng, Gang,Liu, Aiyi,et al. The limiting bound of Efron's W-formula for hypothesis testing when a nuisance parameter is present only under the alternative[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE,2010,140(6):1610-1617.
APA	Li, Qizhai,Zheng, Gang,Liu, Aiyi,Xiong, Shifeng,Li, Zhaohai,&Yu, Kai.(2010).The limiting bound of Efron's W-formula for hypothesis testing when a nuisance parameter is present only under the alternative.JOURNAL OF STATISTICAL PLANNING AND INFERENCE,140(6),1610-1617.
MLA	Li, Qizhai,et al."The limiting bound of Efron's W-formula for hypothesis testing when a nuisance parameter is present only under the alternative".JOURNAL OF STATISTICAL PLANNING AND INFERENCE 140.6(2010):1610-1617.