Asymptotically Stable Tests with Application to Robust Detection

Abstract

To design highly robust and efficient tests, a new method based on the so-called variational optimization approach for robust estimation proposed by Shurygin (1994a, b) is developed. A new indicator of robustness of tests, the test stability, is introduced. The optimal decision rules maximizing test efficiency under the guaranteed level of test stability are written out. The proposed stable tests are based on redescending M-estimators as the corresponding test statistics. For hypothesis testing of location, one of those tests, namely a radical test, outperforms the conventional robust linear bounded Huber’s and redescending Hampel’s tests under heavy-tailed distributions although being slightly inferior to Huber’s test under the Gaussian and moderately contaminated Gaussian distributions.