Robust Regression

Analysis and Applications

Kenneth D. Lawrence

• Publisher: CRC Press
• Year: 2019
• Print ISBN: 9780367580186
• eBook ISBN: 9781351418270
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Robust Regression: Analysis and Applications characterizes robust estimators in terms of how much they weight each observation discusses generalized properties of Lp-estimators. Includes an algorithm for identifying outliers using least absolute value criterion in regression modeling reviews redescending M-estimators studies Li linear regression proposes the best linear unbiased estimators for fixed parameters and random errors in the mixed linear model summarizes known properties of Li estimators for time series analysis examines ordinary least squares, latent root regression, and a robust regression weighting scheme and evaluates results from five different robust ridge regression estimators.

Part I

Advances in Robust Regression

1

The Weighting Pattern of a Bayesian Robust Estimator

GINA G. CHEN Hewlett-Packard, Rockaway, New Jersey

GEORGE P. BOX University of Wisconsin-Madison, Madison, Wisconsin

1. INTRODUCTION

Data has frequently been analyzed as if, to an adequate approximation, errors are normally, identically, and independently distributed. Because it has come to be believed that the first two of the assumptions are frequently inappropriate and in fact that error distributions are likely to be leptokurtic and/or contaminated by occasional bad values giving rise to outliers, attention has been directed, in particular by Huber (1972), Andrews et al. (1972), Hogg (1974), and Barnett and Lewis (1978), to various estimators which are insensitive to such departures.

Such procedures usually give smaller weights to observations that appear discrepant and so can be characterized by their weighting patterns.

In Sections 2 and 3 the structure of certain robust Bayesian estimators is examined from this point of view, and in Section 4 the weighting pattern for a robust Bayesian posterior mean is compared with those for some M-estimators.

2. A BAYESIAN APPROACH TO ROBUST ESTIMATION

Consider the linear model

$\text{Y}=\text{X}\theta +\text{e}$

where Υ is an n × 1 vector of observations, Χ an n × ℓ matrix of fixe...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Preface
• Table of Contents
• Contributors
• Part I Advances in Robust Regression
• Part II Robust Regression Methods
• Part III Forecasting and Robust Regression
• Part IV Robust Ridge Regression
• Index