Nonparametric Statistical Methods Using R, 2nd Edition

8Topics in Regression

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.

8.1 Introduction

Let $\mathit{Y}=[Y_1,\dots ,Y_n{]}^T$ denote an $n\times 1$ vector of responses. Then the matrix version of the linear model (4.11) is

$\begin{array}{l}\mathit{Y}=\alpha \mathbf{1}+\mathit{X}\mathit{\beta }+\mathit{e}\end{array}$(8.1)

where $\mathit{X}=[{\mathit{x}}_1,\dots ,{\mathit{x}}_n{]}^T$ is an $n\times p$ design matrix, and $\mathit{e}=[e_1,\dots ,e_n{]}^T$ is an $n\times 1$ vector of error terms. Assume for discussion that $f(t)$