[PAST EVENT] Mathematics Colloquium and EXTREEMS-QED Lecture: Cyrus DiCiccio (Stanford University)
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Mathematics Colloquium and EXTREEMS-QED Lecture: Cyrus DiCiccio (Stanford University)
Title: Robust permutation tests for two-sample problems
Abstract: Permutation tests, which are used in a wide range of applications, are valued for their performance in small sample settings where traditional asymptotic tests can have poor performance. When conducted appropriately, permutation tests are "exact" in the sense that the probability of rejecting the null hypothesis, when in fact the null hypothesis is true, is exactly the nominal level, regardless of the sample size. However, permutation tests rely on stringent assumptions about the null hypothesis. A consequence is that these tests may not be valid (even asymptotically) for the hypothesis that researchers are interested in and may not allow researchers to draw meaningful conclusions about their data. This talk addresses the limitations of permutation tests (in the context of two sample problems, as well as dependent data problems) and develops methods that are valid under relaxed assumptions.