Robust estimation of dimension reduction space

Authors:
P. íek;W. Härdle
Affiliations:
Department of Econometrics & OR, Tilburg University, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands;Institut für Statistik und Ökonometrie, Humboldt-Universität zu Berlin, Spandauer Str. 1, D-10178 Berlin, Germany
Venue:
Computational Statistics & Data Analysis
Year:
2006

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Abstract

Most dimension reduction methods based on nonparametric smoothing are highly sensitive to outliers and to data coming from heavy-tailed distributions. Two recently proposed methods, minimum average variance estimation and outer product of gradients, can be and are made robust in such a way that preserves all advantages of the original approach. Their extension based on the local one-step M-estimators is sufficiently robust to outliers and data from heavy-tailed distributions, it is relatively easy to implement, and surprisingly, it performs as well as the original methods when applied to normally distributed data.