The Annals of Statistics

On Inconsistent $M$-Estimators

D. A. Freedman and P. Diaconis

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 10, Number 2 (1982), 454-461.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345786

Digital Object Identifier
doi:10.1214/aos/1176345786

Mathematical Reviews number (MathSciNet)
MR653520

Zentralblatt MATH identifier
0496.62034

JSTOR
links.jstor.org

Subjects
Primary: 62F35: Robustness and adaptive procedures
Secondary: 62E20: Asymptotic distribution theory

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

Citation

Freedman, D. A.; Diaconis, P. On Inconsistent $M$-Estimators. Ann. Statist. 10 (1982), no. 2, 454--461. doi:10.1214/aos/1176345786. https://projecteuclid.org/euclid.aos/1176345786


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