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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)

- Dmitrii Zholud
- 2009

This thesis presents results in Extreme Value Theory with application to Bioinformatics. First, we obtain the asymptotic behavior of the probability of high level excursions for the maximum of the Wiener process increments, followed by the normalization sequence for the corresponding limiting Gumbel distribution. Next, we consider the Shepp statistics for… (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)

- Dmitrii Zholud
- 2011

- Holger Rootzén, Dmitrii Zholud
- Technometrics
- 2016

Disclaimer: This is a version of an unedited manuscript that has been accepted for publication. As a service to authors and researchers we are providing this version of the accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proof will be undertaken on this manuscript before final publication of the Version of Record (VoR).… (More)

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