Summary

Tradition and ease of computation have made the least squares method the most popular form of regression analysis. But in the presence of outliers - errors or exceptional observations - that occur frequently in real data, the least squares method becomes unreliable. To remedy this problem, robust statistical techniques have been developed that can isolate or identify outliers. Robust Regression and Outlier Detection provides the first introduction to these techniques, with an emphasis on 'high-breakdown' methods that cope with a sizable fraction of contamination. It focuses on the least median of squares method, which appeals to the intuition and is easy to use.

Robust Regression and Outlier Detection emphasizes simple, intuitive ideas and their application in actual use. No prior knowldege of the field is required.

The first chapter introduces outliers and robustness in regression. Succeeding chapters discuss simple regression, robust multiple regression, the special case of one-dimensional location, and outlier diagnostics. The final chapter presents an outlook of robustness in related fields such as time series analysis and the estimation of multivariate location and covariance matrices applied to the detection of leverage points.

Every chapter contains exercises, ranging from simple questions to small data sets with clues to their analysis. Coverage is enhanced by over 300 references and numerous figures and examples.

Robust Regression and Outlier Detection is a clear, elementary introduction to these important techniques that will appeal not only to statisticians, but to anyone using regression analysis.

Table of contents

1. Introduction
   1. Outliers in Regression Analysis
   2. The Breakdown Point and Robust Estimators
   Exercises and Problems
   
   
2. Simple Regression
   1. Motivation
   2. Computation of the Least Median of Squares Line
   3. Interpretation of the Results
   4. Examples
   5. An Illustration of the Exact Fit Property
   6. Simple Regression Through the Origin
   7. Other Robust Techniques for Simple Regression
   Exercises and Problems
   
   
3. Multiple Regression
   1. Introduction
   2. Computation of Least Median of Squares Multiple Regression
   3. Examples
   4. Properties of the LMS, the LTS, and S-Estimators
   5. Relation with Projection Pursuit
   6. Other Approaches to Robust Multiple Regression
   Exercises and Problems
   
   
4. The Special Case of One-Dimensional Location
   1. Location as a Special Case of Regression
   2. The LMS and the LTS in One Dimension
   3. Use of the Program PROGRESS
   4. Asymptotic Properties
   5. Breakdown Points and Averaged Sensitivity Curves
   Exercises and Problems
   
   
5. Algorithms
   1. Structure of the Algorithm Used in PROGRESS
   2. Special Algorithms for Simple Regression
   3. Other High-Breakdown Estimators
   4. Some Simulation Results
   Exercises and Problems
   
   
6. Outlier Diagnostics
   1. Introduction
   2. The Hat Matrix and LS Residuals
   3. Single-Case Diagnostics
   4. Multiple-Case Diagnostics
   5. Recent Developments
   6. High-Breakdown Diagnostics
   Exercises and Problems
   
   
7. Related Statistical Techniques
   1. Robust Estimation of Multivariate Location and Covariance Matrices, Including the Detection of Leverage Points
   2. Robust time Series Analysis
   3. Other Techniques
   Exercises and Problems
   
   

Book details

Wiley-Interscience, New York (Series in Applied Probability and Statistics), 329 pages.
ISBN 0-471-85233-3.
Fourth printing, 17 reviews.

Software incorporation

PROGRESS (LMS and LTS regression)

• in S-PLUS (as the functions lmsreg and ltsreg)
• in SAS/IML Version 6.12 and later (as the calls LMS and LTS)

• in S-PLUS (as the function cov.mve)
• in SAS/IML Version 6.12 and later (as the call MVE)

Programs