KMS Of Academy of mathematics and systems sciences, CAS
| The limiting bound of Efron's W-formula for hypothesis testing when a nuisance parameter is present only under the alternative | |
Li, Qizhai1 ; Zheng, Gang2; Liu, Aiyi3; Xiong, Shifeng1; Li, Zhaohai4,5; Yu, Kai4
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| 2010-06-01 | |
| Source Publication | JOURNAL OF STATISTICAL PLANNING AND INFERENCE
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| ISSN | 0378-3758 |
| Volume | 140Issue:6Pages:1610-1617 |
| Abstract | 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. |
| Keyword | Hypothesis testing Limiting bound MAX Nuisance parameter Robustness W-formula |
| DOI | 10.1016/j.jspi.2009.12.021 |
| Language | 英语 |
| Funding Project | National Institutes of Health ; National Young Science Foundation of China[10901155] |
| WOS Research Area | Mathematics |
| WOS Subject | Statistics & Probability |
| WOS ID | WOS:000275345500022 |
| Publisher | ELSEVIER SCIENCE BV |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/10423 |
| Collection | 系统科学研究所 |
| Corresponding Author | Li, Qizhai |
| Affiliation | 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 |
| Recommended Citation 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. |
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