On Inconsistent $M$-Estimators

D. A. Freedman; P. Diaconis

doi:10.1214/aos/1176345786

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Home > Journals > Ann. Statist. > Volume 10 > Issue 2 > Article

June, 1982 On Inconsistent $M$-Estimators

D. A. Freedman, P. Diaconis

Ann. Statist. 10(2): 454-461 (June, 1982). DOI: 10.1214/aos/1176345786

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Abstract

If $M$ is not convex, and the underlying density is multi-modal, $M$-estimators can be inconsistent. Examples are given, as well as some positive results.