Asymptotically Stable Tests with Application to Robust Detection
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.
KeywordsScore Function Stable Estimation Asymptotic Variance Noise Distribution Monte Carlo Experiment
I would like to thank the referees for their important and helpful comments. Also I am so much grateful to Prof. Ayanendranath Basu for his patience and help, which allowed me to finalize this paper.
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