Journal
JOURNAL OF STATISTICAL PLANNING AND INFERENCE
Volume 143, Issue 11, Pages 1968-1979Publisher
ELSEVIER
DOI: 10.1016/j.jspi.2013.06.011
Keywords
Data-adaptive multiple test; False discovery rate; Family wise error rate; Quantile transformation; Schweder-Spjotvoll estimator; Simultaneous statistical inference
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We are considered with the problem of m simultaneous statistical test problems with composite null hypotheses. Usually, marginal p-values are computed under least favorable parameter configurations (LFCs), thus being over-conservative under non-LFCs. Our proposed randomized p-value leads to a tighter exhaustion of the marginal (local) significance level. In turn, it is stochastically larger than the LFC-based p-value under alternatives. While these distributional properties are typically nonsensical for m=1, the exhaustion of the local significance level is extremely helpful for cases with m>1 in connection with data-adaptive multiple tests as we will demonstrate by considering multiple one-sided tests for Gaussian means. (C) 2013 Elsevier B.V. All rights reserved.
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