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Robust bounded-influence tests in general parametric models. (English) Zbl 0804.62037
Summary: We introduce robust tests for testing hypotheses in a general parametric model. These are robust versions of the Wald, scores, and likelihood ratio tests and are based on general $$M$$ estimators. Their asymptotic properties and influence functions are derived. It is shown that the stability of the level is obtained by bounding the self-standardized sensitivity of the corresponding $$M$$ estimator. Furthermore, optimally bounded-influence tests are derived for the Wald- and scores-type tests. Applications to real and simulated data sets are given to illustrate the tests’ performance.

MSC:
 62F35 Robustness and adaptive procedures (parametric inference) 62F03 Parametric hypothesis testing
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