Robust Line Estimation with Errors in Both Variables

Abstract

The estimator holding the central place in the theory of the multivariate “errors-in-the-variables” (EV) model results from performing orthogonal regression on variables rescaled according to the covariance matrix of the errors. Our simulations on the univariate model essentially relegate this estimator to use only in large samples on data with no trace of outlier contamination. A modification requiring a robust preliminary slope is proposed that essentially sets out the generalization to EV of the robust w -estimator in regression. It is demonstrated that the modification is robust to outlier contamination even in small samples, given a sufficiently good preliminary estimator. Candidates for a preliminary slope estimator based on the data are discussed and the performance of one under simulation is examined.