High-Breakdown Rank Regression
提出一种具有50%崩溃点且渐近正态的加权秩估计，基于此开发推断和诊断方法，在抗离群高杠杆簇方面接近最小中位数平方，且比仅校正因子空间的广义秩估计更有效。
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.