Bounded-Influence Rank Regression: A One-Step Estimator Based on Wilcoxon Scores
将Krasker-Welsch的有界影响方法与秩回归结合，提出一种基于Wilcoxon得分的一步估计量，通过权重降低异常值影响，并证明其一致性和渐近正态性。
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.