Bounded-Influence Rank Regression: A One-Step Estimator Based on Wilcoxon Scores

Abstract

The Krasker-Welsch (1982) approach to bounding influence is merged with rank regression. I propose a one-step estimator that is analogous to Bickel's (1975) one-step M estimator of Type 1 but uses weights that depend on the design vector and the residuals to reduce the influence of outliers. In fact, the standardized sensitivity of the estimator is made equal to a prechosen constant. It is based, however, on a second-derivative approximation to a dispersion surface that is not convex. This one-step variant avoids the problem of multiple roots. The estimator is shown to be consistent and asymptotically multivariate normal. An example shows that it yields results similar to those of the Krasker-Welsch estimator.

Key Words:

• Influence function
• Sensitivity
• Wilcoxon signed rank statistic