Nonparametric Statistical Methods Using R

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 $\mathit{Y}={\left[y_1,...y_n\right]}^T$ denote an n × 1 vector of responses. Then the matrix version of the linear model, (4.2), is

$\mathit{Y}=\alpha 1+\mathit{X}\beta +e(7.1)$

where $X={\left[x_1,...,x_n\right]}^T$ is an n × p design matrix, and $\mathit{e}={\left[e_1,...,e_n\right]}^T$ is an n × 1 vector of error terms. Assume for ...