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Nonparametric Statistical Methods Using R by Joseph W. McKean, John Kloke

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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 Y=[ y1,...yn ]T denote an n × 1 vector of responses. Then the matrix version of the linear model, (4.2), is

Y=α1+Xβ+e    (7.1)

where X=[ x1,...,xn ]T is an n × p design matrix, and e=[ e1,...,en ]T is an n × 1 vector of error terms. Assume for ...

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