A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Sets
This work addresses a practical problem in statistics for scenarios with limited data, but it is incremental as it builds on existing robust testing methods.
The paper tackles robust hypothesis testing for small-sample scenarios by proposing a data-driven method using Sinkhorn distance to create distributional uncertainty sets, resulting in a more flexible detector that shows competitive performance in numerical experiments on synthetic and real datasets.
Hypothesis testing for small-sample scenarios is a practically important problem. In this paper, we investigate the robust hypothesis testing problem in a data-driven manner, where we seek the worst-case detector over distributional uncertainty sets centered around the empirical distribution from samples using Sinkhorn distance. Compared with the Wasserstein robust test, the corresponding least favorable distributions are supported beyond the training samples, which provides a more flexible detector. Various numerical experiments are conducted on both synthetic and real datasets to validate the competitive performances of our proposed method.