Multiple Testing Procedures under dependence, with applications
Alessio Farcomeni
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Multiple Testing Procedures under dependence, with applications

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Multiple hypothesis testing is concerned with maintaining low the number of false positives when testing several hypotheses simultaneously, while achieving a number of false negatives as small as possible. Procedures should be distribution free and robust with respect to known or possibly unknown dependence. This thesis is related to modern approaches. After a review of the most recent developments, we prove robustness of certain procedures under weak dependence. We then propose a new class of procedures and estimators for the proportion of false null hypotheses, i.e., the strength of the simo...