BOUNDED INFLUENCE RANK REGRESSION

When epsilon(i)=y(i)-x(i)'beta, it is known that minimizing SIGMASIGMA \epsilon(i) - epsilon(j)\ yields an estimate of regression that attain s a bounded influence of the residual with 95% efficiency for the norm al distribution. We show that introducing weights SIGMASIGMAb(ij)\epsi lon(i)-epsilon(j)\ achieves bounded total influence with positive brea kdown. Mallows weights in particular are optimally efficient under a p redefined bound on the gross error sensitivity. A generalization of Ma llows weights allows additional local stability against high leverage points. Two numerical examples illustrate the behaviour of the estimat e.