Abstract
Starting from the robust Wald- and score-type tests, we construct a new robust test in general parametric models based on general M-estimators, so-called robust gradient-type test. The asymptotic properties of the robust gradient-type test statistic under the null hypothesis and under a sequence of contiguous alternatives are derived. The local stability of its asymptotic level under contamination is investigated. An optimal bounded-influence test for the robust gradient-type test is also discussed.
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