Approximate τ—Estimates for Linear Regression Based on Subsampling of Elemental Sets

In this paper we show that approximate τ-estimates for the linear model, computed by the algorithm based on subsampling of elemental subsets, are consistent and with high probability have the same breakdown point that the exactτ-estimate. Then, if these estimates are used as initial values, the reweighted least squares algorithm yields a local minimum of the τ-scale having the same asymptotic distribution and, with high probability, the same breakdown point that the global minimum.