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This paper develops tail estimation methods to handle false positives in multiple testing problems where testing is done at extreme significance levels and with low degrees of freedom, and where the true null distribution may differ from the theoretical one. We show that the number of false positives, conditional on the total number of positives,(More)
We prove continuity of the limit distribution function of certain multiscale test statistics which are used in nonparametric curve estimation. A particular variant of multiscale testing was introduced in Dümbgen and Spokoiny (2001) in order to test qualitative hypotheses about an unknown regression function such as nonpositivity, monotonicity or concavity.(More)
This material contains introduction to the SmartTail software; proofs of Theorems 1, 2, and 3 in the paper; derivation of equation (10); additional results and discussion for dependent p-values; sandwich estimators for dependent p-values; additional plots for the yeast genome and salt stress screening data; and two additional examples: association mapping(More)
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