Robust estimation in the errors-in-variables model

Abstract

Orthogonal regression analogues of M estimates of regression, called here orthogonal regression M estimates, are defined. These estimates are shown to be consistent at elliptical errors-in-variables models and robust, if the corresponding loss function is bounded. The orthogonal regression analogues of regression scale estimates, called here orthogonal regression S estimates, are considered as well. In particular, they provide a robust estimate for the scale of the orthogonal residuals, a crucial quantity in the computation of orthogonal regression M estimates. Finally we present an algorithm for computing orthogonal regression S and M estimates and the results of a small Monte Carlo experiment.