Optimal Bias Robust M—estimates of Regression

Abstract

We find a family of M-estimates of regression with the following minimax bias property: They minimize the asymptotic variance at the central model subject to a bound on the maximum bias over contamination neighborhoods. For the case of multivariate normal data, the optimal ψ-functions associated with the optimal estimates are numerically computed. A comparison of the optimal estimate with the locally optimal estimate of Yohai and Zamar and the estimate based on Tukey's bisquare score function is also presented.