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Journal of Statistical Theory and Practice

, Volume 4, Issue 1, pp 155–167 | Cite as

Probabilistic Set-membership Approach for Robust Regression

  • Luc Jaulin
Article

Abstract

Interval constraint propagation methods have been shown to be efficient and reliable to solve difficult nonlinear bounded-error estimation problems. However they are considered as unsuitable in a probabilistic context, where the approximation of a probability density function by a set cannot be accepted as reliable. This paper shows how probabilistic estimation problems can be transformed into a set estimation problem by assuming that some rare events will never happen. Since the probability of occurrence of those rare events can be computed, we can give some prior lower bounds for the probability associated to solution set of the corresponding set estimation problem. The approach will be illustrated on a parameter estimation problem.

AMS Subject Classification

65G99 

Keywords

Interval analysis Probability Robust regression Set-membership estimation 

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Copyright information

© Grace Scientific Publishing 2010

Authors and Affiliations

  1. 1.ENSIETA, DTNBrest Cédex 09France

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