Kernel Robust Hypothesis Testing

Topics in kernel hypothesis testing

This thesis investigates some unaddressed problems in kernel nonparametrichypothesis testing. The contributions are grouped around three main themes:Wild Bootstrap for Degenerate Kernel Tests. A wild bootstrap method for non-parametric hypothesis tests based on kernel distribution embeddings is pro-posed. This bootstrap method is used to construct provably consistent teststh...

Asymptotically Minimax Robust Hypothesis Testing

The design of asymptotically minimax robust hypothesis testing is formalized for the Bayesian and Neyman-Pearson tests of Type I and II. The uncertainty classes based on the KL-divergence, αdivergence, symmetrized α-divergence, total variation distance, as well as the band model, moment classes and p-point classes are considered. It is shown with a counterexample that minimax robust tests do no...

Robust Performance Hypothesis Testing with the Variance

Applied researchers often test for the difference of the variance of two investment strategies; in particular, when the investment strategies under consideration aim to implement the global minimum variance portfolio. A popular tool to this end is the F -test for the equality of variances. Unfortunately, this test is not valid when the returns are correlated, have tails heavier than the normal ...

Robust Hypothesis Testing via Lq-Likelihood

This article introduces a robust hypothesis testing procedure: the Lq-likelihoodratio-type test (LqRT). By deriving the asymptotic distribution of this test statistic, the authors demonstrate its robustness both analytically and numerically, and they investigate the properties of both its influence function and its breakdown point. A proposed method to select the tuning parameter q offers a goo...

A note on robust hypothesis testing