Robust bounded-influence tests in general parametric models

Stéphane Heritier, Elvezio Ronchetti

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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.

Original languageEnglish
Pages (from-to)897-904
Number of pages8
JournalJournal of the American Statistical Association
Issue number427
Publication statusPublished - 1 Jan 1994


  • Fréchet differentiability
  • Influence function
  • Logistic regression
  • M estimators
  • Scores test
  • Wald test

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