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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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