To how many simultaneous hypothesis tests can normal, student's t or bootstrap calibration be applied?

doi:10.1198/016214507000000969

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	To how many simultaneous hypothesis tests can normal, student's t or bootstrap calibration be applied?
	Fan, Jianqing 1,3; Hall, Peter 2,3; Yao, Qiwei 3
	2007-12-01
发表期刊	JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN	0162-1459
卷号	102 期号:480 页码:1282-1288
摘要	In the analysis of microarray data, and in some other contemporary statistical problems, it is not uncommon to apply hypothesis tests in a highly simultaneous way. The number, N say, of tests used can be much larger than the sample sizes, n, to which the tests are applied, yet we wish to calibrate the tests so that the overall level of the simultaneous test is accurate. Often the sampling distribution is quite different for each test, so there may not be an opportunity to combine data across samples. In this setting, how large can N be, as a function of n, before level accuracy becomes poor? Here we answer this question in cases where the statistic under test is of Student's t type. We show that if either the normal or Student t distribution is used for calibration, then the level of the simultaneous test is accurate provided that log N increases at a strictly slower rate than n(1/3) as n diverges. On the other hand, if bootstrap methods are used for calibration, then we may choose log N almost as large as n(1/2) and still achieve asymptotic-level accuracy. The implications of these results are explored both theoretically and numerically.
关键词	Bonferroni's inequality edgeworth expansion genetic data large-deviation expansion level accuracy microarray data quantile estimation skewness student's t statistic
DOI	10.1198/016214507000000969
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000251829200022
出版者	AMER STATISTICAL ASSOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5244
专题	中国科学院数学与系统科学研究院
通讯作者	Fan, Jianqing
作者单位	1.Princeton Univ, Dept Operat Res & Financial Engn, Princeton, NJ 08544 USA 2.Acad Math & Syst Sci, Ctr Stat Res, Beijing, Peoples R China 3.Univ Melbourne, Dept Math Stat, Melbourne, Vic 3010, Australia
推荐引用方式 GB/T 7714	Fan, Jianqing,Hall, Peter,Yao, Qiwei. To how many simultaneous hypothesis tests can normal, student's t or bootstrap calibration be applied?[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,2007,102(480):1282-1288.
APA	Fan, Jianqing,Hall, Peter,&Yao, Qiwei.(2007).To how many simultaneous hypothesis tests can normal, student's t or bootstrap calibration be applied?.JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,102(480),1282-1288.
MLA	Fan, Jianqing,et al."To how many simultaneous hypothesis tests can normal, student's t or bootstrap calibration be applied?".JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 102.480(2007):1282-1288.