Open Access
June, 1982 On Inconsistent $M$-Estimators
D. A. Freedman, P. Diaconis
Ann. Statist. 10(2): 454-461 (June, 1982). DOI: 10.1214/aos/1176345786


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.


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D. A. Freedman. P. Diaconis. "On Inconsistent $M$-Estimators." Ann. Statist. 10 (2) 454 - 461, June, 1982.


Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0496.62034
MathSciNet: MR653520
Digital Object Identifier: 10.1214/aos/1176345786

Primary: 62F35
Secondary: 62E20

Keywords: $\psi$-functions , $M$-estimators , consistency , robustness

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • June, 1982
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