Comparison of robust hypothesis tests for fixed sample size and sequential observations

Fixed sample size and sequential performance of the asymptotically minimax robust hypothesis test is evaluated over a signal processing example and the results are compared to other well known robust hypothesis testing schemes and the nominal test. As a fixed sample size test around fifty samples are sufficient to observe the minimax properties of the asymptotically minimax robust test. Comparisons indicate that Huber's minimax robust test and the nominal test degrade their performances drastically when imposed to uncertainties due to modeling errors. Similarly, Dabak and Johnson's asymptotically robust test degrades its performance, hence it is not minimax robust. This indicates that choosing the right uncertainty model and the corresponding minimax test is crucial in applications. For the sequential test a new definition of minimax robustness is made. The simulations indicate that the new definition is satisfied by the asymptotically minimax robust test asymptotically.