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

• 成果类型: Article
• 署名作者: Fan, Jianqing; Hall, Peter; Yao, Qiwei
• 署名单位: Princeton University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; University of Melbourne
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214507000000969
• 发表日期: 2007
• 页码: 1282-1288
• 关键词: false discovery rate; MULTIPLE TEST PROCEDURES; microarray data; large deviation; step-down; i errors; normalization; Consistency; genes; MODEL

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.