ABSTRACT
If we want to test the simple hypothesis P0 against the simple alternative P1, then we use the likelihood ratio test, following the Neyman-Pearson lemma. Following Huber (1965), if the true hypothetical distribution may not be exactly P0 but rather lies in some neighborhood P0 of an idealized simple hypothesis, and similarly the true alternative distribution lies in some neighborhood P1 of a simple alternative P1, one should test robustly P0 against P1, using the maximin likelihood ratio test, based on the least favorable distributions of P0, and P1. Huber and Strassen (1973) extended the robust testing theory to a general class of testing problems, using the concept of Choquet capacities.
