Robust hypothesis testing and distribution estimation in Hellinger distance
This work addresses robust statistical inference for scenarios with distributional uncertainties, though it appears incremental as it builds on existing hypothesis testing frameworks.
The authors tackled robust hypothesis testing under distribution perturbations in Hellinger distance, achieving sample complexity comparable to the optimal Neyman-Pearson test up to constants and demonstrating empirical power on canonical distributions.
We propose a simple robust hypothesis test that has the same sample complexity as that of the optimal Neyman-Pearson test up to constants, but robust to distribution perturbations under Hellinger distance. We discuss the applicability of such a robust test for estimating distributions in Hellinger distance. We empirically demonstrate the power of the test on canonical distributions.