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

ADROVER, JORGE G.; BIANCO, ANA M.; YOHAI, VÍCTOR J.

Statistics in Genetics and in the Environmental Sciences

Springer

Año: 2001; p. 173 - 183

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 withhigh 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 minimumof the τ-scale having the same asymptotic distribution and, with high probability, the same breakdown point that the global minimum.