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• W1787331520 abstract "The false discovery rate (FDR) is widely used and accepted as error criterion in multiple hypothesis testing and much effort has been done to develop multiple tests which control the FDR under different model assumptions. The FDR is often used when the number of false rejections of a multiple test is allowed to be a reasonable portion of all rejections. It is defined as the expected portion of false rejections among all rejections. The most famous multiple test with respect to the FDR is the linear step-up test of Benjamini and Hochberg [2] which controls the FDR under different assumptions, but still does not exhausts it and thus may have a lack of power. Therefore, the adaptive step-up test of Storey et al. [61] has been proposed which includes an estimation of the portion of true null hypotheses. In the introductory first chapter we introduce the basic model assumptions for this thesis and give a brief summary of well known results. Chapter 2 provides three central lemmas from which we derive various results concerning the FDR of non adaptive step-up tests, the critical values of step-up tests with FDR control and the asymptotic FDR of adaptive step-up tests. We consider several dependence structures of the p-values, including independence, a reverse martingale structure, positive regression dependence and arbitrary dependence. In Chapter 3 we extend the results of Storey [59, 60] to p-values of null hypotheses whose marginal distributions are stochastically larger than the uniform distribution on [0,1] which may occur for one sided hypotheses. We motivate a new class of estimators for adaptive step-up tests and show that the common estimation of the portion of true null hypotheses is not appropriate in this case. In Chapter 4 we establish a new sufficient condition for finite sample FDR control of adaptive step-up tests under independence and we prove that a slightly modified estimator from Chapter 3 satisfies this condition. It turns out that the selection of the estimator for the adaptive step-up test may even be performed in a data dependent manner. A reasonable selection method is discussed in a practical guide. Chapter 5 is devoted to finite sample FDR control of adaptive step-up tests under a specific kind of block dependence." @default.
• W1787331520 created "2016-06-24" @default.
• W1787331520 creator A5012734003 @default.
• W1787331520 date "2015-01-01" @default.
• W1787331520 modified "2023-09-27" @default.
• W1787331520 title "Adaptive step up tests for the false discovery rate (FDR) under independence and dependence" @default.
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• W1787331520 hasPublicationYear "2015" @default.
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