In Chapter 4 we introduced rank-based fitting of linear models using Rfit. In this chapter, we discuss further topics for rank-based regression. These include high breakdown fits, diagnostic procedures, weighted regression, nonlinear models, and autoregressive time series models. We also discuss optimal scores for a family of skew normal distributions and present an adaptive procedure for regression estimation based on a family of Winsorized Wilcoxon scores.
Let denote an n × 1 vector of responses. Then the matrix version of the linear model, (4.2), is
where is an n × p design matrix, and is an n × 1 vector of error terms. Assume for ...