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Chapter 7

# Regression II

## 7.1 Introduction

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 $\mathbit{Y}={\left[{y}_{1},...{y}_{n}\right]}^{T}$ denote an n × 1 vector of responses. Then the matrix version of the linear model, (4.2), is

where $X={\left[{x}_{1},...,{x}_{n}\right]}^{T}$ is an n × p design matrix, and $\mathbit{e}={\left[{e}_{1},...,{e}_{n}\right]}^{T}$ is an n × 1 vector of error terms. Assume for ...

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