Permutation-based inference for high-dimensional data.

Abstract

The

thesis provides novel statistical (multiple) testing methods based on

permutations or other transformations of data. Permutation-based multiple

testing methods tend to have relatively high power, because they take into account the observed dependence structure of the data (without requiring assumptions on that structure). This thesis places particular emphasis on confidence upper bounds for the false discovery proportion: the proportion of false positives among all rejected hypotheses. Moreover, a novel semi-parametric method is presented for robust testing in generalized linear models. This test is related to the score test and the permutation test and is based on sign-flipping individual score contributions.