A smoothing principle for the Huber and other location M-estimators

Hampel, Frank R.; Hennig, Christian; Ronchetti, Elvezio

doi:10.1016/j.csda.2010.05.001

Scientific article

English

A smoothing principle for the Huber and other location M-estimators

Contributors

Hampel, Frank R.; Hennig, Christian; Ronchetti, Elvezio

Published in

Computational statistics & data analysis, vol. 55, no. 1, p. 324-337

Publication date

2011

Abstract

A smoothing principle for M-estimators is proposed. The smoothing depends on the sample size so that the resulting smoothed M-estimator coincides with the initial M-estimator when n→∞. The smoothing principle is motivated by an analysis of the requirements in the proof of the Cramér–Rao bound. The principle can be applied to every M-estimator. A simulation study is carried out where smoothed Huber, ML-, and Bisquare M-estimators are compared with their non-smoothed counterparts and with Pitman estimators on data generated from several distributions with and without estimated scale. This leads to encouraging results for the smoothed estimators, and particularly the smoothed Huber estimator, as they improve upon the initial M-estimators particularly in the tail areas of the distributions of the estimators. The results are backed up by small sample asymptotics.

Keywords

Pitman estimator
ML-estimator
Median
MAD
Breakdown point
Small sample asymptotics
Cauchy distribution
Huber's least favourable distribution
Double exponential distribution
Robust estimation

UNIGE affiliation entities

Faculté d'économie et de management / Research Center for Statistics

Citation (ISO format)

HAMPEL, Frank R., HENNIG, Christian, RONCHETTI, Elvezio. A smoothing principle for the Huber and other location M-estimators. In: Computational statistics & data analysis, 2011, vol. 55, n° 1, p. 324–337. doi: 10.1016/j.csda.2010.05.001

Article (Published version)

Identifiers

PID : unige:22889
DOI : 10.1016/j.csda.2010.05.001

Additional URL for this publication

http://linkinghub.elsevier.com/retrieve/pii/S0167947310001878

Journal ISSN

0167-9473

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11/09/2012 19:39:00

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11/09/2012 19:39:00

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31/08/2026 08:50:33

A smoothing principle for the Huber and other location M-estimators

Contributors

Published in

Publication date

Abstract

Keywords

UNIGE affiliation entities

Citation (ISO format)

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Identifiers

Additional URL for this publication

Journal ISSN

Technical informations

Creation

First validation

Update

Status update

Last indexation