A resampling design for computing high-breakdown regression

For the computation of high-breakdown (HB) regression one typically uses an algorithm based on randomly selected p-subsets, where p is the number of parameters. This resampling algorithm may itself break down, with a probability that decreases with the number of p-subsets generated. In order to be certain that this algorithm does not break down, the number of p-subsets needs to be O(np). In this paper a resampling design is proposed such that for fixed p the necessary number of p-subsets is merely O(n). This resampling design can also be used for HB nonlinear regression and for HB estimators of multivariate location and scatter.