Robust hypothesis testing with composite distances

We propose a minimax robust hypothesis testing scheme that involves a composite uncertainty class based on two different distances. The first distance models the misassumptions on the nominal distributions and the second distance models the outliers. We prove that the least favorable distributions, with a desired minimax property, exist for the composite uncertainty class. It is shown that such a construction provides flexibility in designing robust tests, both in terms of the choice of the correct model as well as the clipping thresholds. Experimental results justify the aforementioned assertions.