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ArticleOriginal scientific text

Title

Redescending M-estimators in regression analysis, cluster analysis and image analysis

Authors 1

Affiliations

  1. Carl von Ossietzky University Oldenburg, Institute for Mathematics, Postfach 2503, D-26111 Oldenburg, Germany

Abstract

We give a review on the properties and applications of M-estimators with redescending score function. For regression analysis, some of these redescending M-estimators can attain the maximum breakdown point which is possible in this setup. Moreover, some of them are the solutions of the problem of maximizing the efficiency under bounded influence function when the regression coefficient and the scale parameter are estimated simultaneously. Hence redescending M-estimators satisfy several outlier robustness properties. However, there is a problem in calculating the redescending M-estimators in regression. While in the location-scale case, for example, the Cauchy estimator has only one local extremum this is not the case in regression. In regression there are several local minima reflecting several substructures in the data. This is the reason that the redescending M-estimators can be used to detect substructures in data, i.e. they can be used in cluster analysis. If the starting point of the iteration to calculate the estimator is coming from the substructure then the closest minimum corresponds to this substructure. This property can be used to construct an edge and corner preserving smoother for noisy images so that there are applications in image analysis as well.

Keywords

ENG
redescending M-estimator, regression, breakdown point, optimality, cluster analysis, image analysis, kernel estimator

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Discussiones Mathematicae Probability and Statistics
2004/24/1
Export to PBN, Opens in new tab
Pages:
59-75
Main language of publication
English
Received
2003-10-04
Published
2004

DOI: 10.7151/dmps.1046

Exact and natural sciences