Marco Cattaneo, Andrea Wiencierz

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Regression with Imprecise Data: A Robust Approach

Abstract

We introduce a robust regression method for imprecise data, and apply it to social survey data. Our method combines nonparametric likelihood inference with imprecise probability, so that only very weak assumptions are needed and different kinds of uncertainty can be taken into account. The proposed regression method is based on interval dominance: interval estimates of quantiles of the error distribution are used to identify plausible descriptions of the relationship of interest. In the application to social survey data, the resulting set of plausible descriptions is relatively large, reflecting the amount of uncertainty inherent in the analyzed data set.

Keywords

Robust regression, imprecise data, nonparametric statistics, likelihood inference, imprecise probability distributions, survey data, informative coarsening, complex uncertainty, interval dominance, identification regions.

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Authors’ addresses

Marco Cattaneo
Institut fuer Statistik
Ludwig-Maximilians-Universitaet Muenchen
Ludwigstrasse 33
80539 Muenchen

Andrea Wiencierz
Department of Statistics, LMU Munich
Ludwigstr. 33
80539 Munich
Germany

E-mail addresses

Marco Cattaneo		cattaneo@stat.uni-muenchen.de
Andrea Wiencierz		Andrea.Wiencierz@stat.uni-muenchen.de