Fast and robust estimation of the multivariate errors in variables model.

Abstract

In the multivariate errors in variable models one wishes to retrieve a linear relationship of the form y = ß x + a, where both x and y can be multivariate. The variables y and x are not directly measurable, but observed with measurement error. The classical approach to estimate the multivariate errors in variable model is based on an eigenvector analysis of the joint covariance matrix of the observations. In this paper a projection-pursuit approach is proposed to estimate the unknown parameters. Focus is on projection indices based on half-samples. These will lead to robust estimators, which can be computed using fast algorithms. Consistency of the procedure is shown, without needing to make distributional assumptions on the x-variables. A simulation study gives insight in the robustness and the efficiency of the procedure.Algorithms; Consistency; Covariance; Efficiency; Errors in variables; Estimator; Matrix; Measurement; Model; Models; Multivariate statistics; Principal component analysis; Projection-pursuit; Robust estimation; Robustness; Simulation; Studies; Variables;