To how many simultaneous hypothesis tests can normal, student's t or bootstrap calibration be applied?
文献类型：期刊论文
| 作者 | Fan, Jianqing1,3; Hall, Peter2,3; Yao, Qiwei3 |
| 刊名 | JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
 |
| 出版日期 | 2007-12-01 |
| 卷号 | 102期号:480页码:1282-1288 |
| 关键词 | Bonferroni's inequality edgeworth expansion genetic data large-deviation expansion level accuracy microarray data quantile estimation skewness student's t statistic |
| ISSN号 | 0162-1459 |
| DOI | 10.1198/016214507000000969 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000251829200022 |
| 出版者 | AMER STATISTICAL ASSOC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/5243]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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