Robust weighted orthogonal regression in the errors-in-variables model

Authors:
M. Fekri;A. Ruiz-Gazen
Affiliations:
Département d'Informatique et de Mathématiques Appliquées, INPT, Maroc and Laboratoire de Statistique et Probabilités, UMR CNRS C5583, Université Paul Sabatier, Toulouse c ...;Laboratoire de Statistique et Probabilités, UMR CNRS C5583, Université Paul Sabatier and GREMAQ, UMR CNRS C5604, Université de Sciences Sociales de Toulouse 1, 31000 Toulouse, Franc ...
Venue:
Journal of Multivariate Analysis
Year:
2004

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Abstract

This paper focuses on robust estimation in the structural errors-in-variables (EV) model. A new class of robust estimators, called weighted orthogonal regression estimators, is introduced. Robust estimators of the parameters of the EV model are simply derived from robust estimators of multivariate location and scatter such as the M-estimators, the S-estimators and the MCD estimator. The influence functions of the proposed estimators are calculated and shown to be bounded. Moreover, we derive the asymptotic distributions of the estimators and illustrate the results on simulated examples and on a real-data set.