Fast and robust estimation of the multivariate errors in variables model

In the multivariate errors in variables models, one wishes to retrieve a linear relationship of the form y=βtx+α, 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 variables 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. The focus is on projection indices based on half-samples. These lead to robust estimators which can be computed using fast algorithms. Fisher consistency of the procedure is shown, without the need to make distributional assumptions on the x-variables. A simulation study gives insight into the robustness and the efficiency of the procedure.