High-Breakdown Rank Regression

Abstract

A weighted rank estimate is proposed that has 50% breakdown and is asymptotically normal at rate √n. Based on this theory, inferential procedures, including asymptotic confidence and tests, and diagnostic procedures, such as studentized residuals, are developed. The influence function of the estimate is derived and shown to be continuous and bounded everywhere in (x, Y) space. Examples show that robustness against outlying high-leverage clusters may approach that of the least median of squares, while retaining more stability against inliers. The estimator uses weights that correct for both factor and response spaces. A Monte Carlo study shows that the estimate is more efficient than the generalized rank estimates, which are generalized R estimates with weights that only correct for factor space. When weights are constant, the estimate reduces to the regular Wilcoxon rank estimate.

Key Words:

• 50% breakdown
• Generalized rank estimate
• Inlier stability
• Least median of squares
• Rank regression
• Weights