  The minimax robust hypothesis testing problem for the case where the nominal
probability distributions are subject to both modeling errors and outliers is
studied in twofold. First, a robust hypothesis testing scheme based on a
relative entropy distance is designed. This approach provides robustness with
respect to modeling errors and is a generalization of a previous work proposed
by Levy. Then, it is shown that this scheme can be combined with Huber's robust
test through a composite uncertainty class, for which the existence of a saddle
value condition is also proven. The composite version of the robust hypothesis
testing scheme as well as the individual robust tests are extended to fixed
sample size and sequential probability ratio tests. The composite model is
shown to extend to robust estimation problems as well. Simulation results are
provided to validate the proposed assertions.
