Introduction to Robust Estimation and Hypothesis Testing

3rd Edition

Authors: Rand Wilcox
Hardcover ISBN: 9780123869838
eBook ISBN: 9780123870155
Imprint: Academic Press
Published Date: 29th December 2011
Page Count: 608
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Table of Contents


Chapter 1. Introduction

1.1 Problems with Assuming Normality

1.2 Transformations

1.3 The Influence Curve

1.4 The Central Limit Theorem

1.5 Is the ANOVA F Robust?

1.6 Regression

1.7 More Remarks

1.8 Using the Computer: R

1.9 Some Data Management Issues

Chapter 2. A Foundation for Robust Methods

2.1 Basic Tools for Judging Robustness

2.2 Some Measures of Location and Their Influence Function

2.3 Measures of Scale

2.4 Scale Equivariant M-Measures of Location

2.5 Winsorized Expected Values

Chapter 3. Estimating Measures of Location and Scale

3.1 A Bootstrap Estimate of a Standard Error

3.2 Density Estimators

3.3 The Sample Trimmed Mean

3.4 The Finite Sample Breakdown Point

3.5 Estimating Quantiles

3.6 An M-Estimator of Location

3.7 One-Step M-estimator

3.8 W-estimators

3.9 The Hodges–Lehmann Estimator

3.10 Skipped Estimators

3.11 Some Comparisons of the Location Estimators

3.12 More Measures of Scale

3.13 Some Outlier Detection Methods

3.14 Exercises

Chapter 4. Confidence Intervals in the One-Sample Case

4.1 Problems when Working with Means

4.2 The g-and-h Distribution

4.3 Inferences About the Trimmed and Winsorized Means

4.4 Basic Bootstrap Methods

4.5 Inferences About M-Estimators

4.6 Confidence Intervals for Quantiles

4.7 Empirical Likelihood

4.8 Concluding Remarks

4.9 Exercises

Chapter 5. Comparing Two Groups

5.1 The Shift Function

5.2 Student’s t-test

5.3 Comparing Medians and Other Trimmed Means

5.4 Inferences Based on a Percentile Bootstrap Method

5.5 Comparing Measures of Scale

5.6 Permutation Tests

5.7 Inferences About a Probabilistic Measure of Effect Size

5.8 Comparing Two Independent Binomial


This revised book provides a thorough explanation of the foundation of robust methods, incorporating the latest updates on R and S-Plus, robust ANOVA (Analysis of Variance) and regression. It guides advanced students and other professionals through the basic strategies used for developing practical solutions to problems, and provides a brief background on the foundations of modern methods, placing the new methods in historical context. Author Rand Wilcox includes chapter exercises and many real-world examples that illustrate how various methods perform in different situations.

Introduction to Robust Estimation and Hypothesis Testing, Second Edition, focuses on the practical applications of modern, robust methods which can greatly enhance our chances of detecting true differences among groups and true associations among variables.

Key Features

  • Covers latest developments in robust regression
  • Covers latest improvements in ANOVA
  • Includes newest rank-based methods
  • Describes and illustrated easy to use software


Advanced graduate students interested in applying cutting-edge methods for analyzing data. Also, any applied researcher who uses ANOVA or regression will benefit. A typical course would be Quantitative Methods found in Mathematics, Economics, Health and Biological Sciences and Psychology departments


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"...Wilcox has greatly enhanced this book, which is now almost twice as large as the first edition. This would now seem to be a good book for everyone to have in their library." --Technometrics, 2005

"This text focuses on applied aspects of major modern and robust statistical methods. Early chapters explain the aims and mathematical foundations of modern methods. The heart of the book describes methods for addressing common problems in ANOVA and regression, with a minimum of technical details, and judges their merits using multiple criteria, giving advice on which ones to use for various situations. Chapter exercises are included. The book assumes a previous introductory statistics course and background on basics of ANOVA, hypothesis testing, and regression. For this third edition, S-PLUS functions are no longer supported. Instead, R functions are supplied." --Reference and Research Book News, Inc.

About the Authors

Rand Wilcox Author

Rand R. Wilcox has a Ph.D. in psychometrics, and is a professor of psychology at the University of Southern California. Wilcox's main research interests are statistical methods, particularly robust methods for comparing groups and studying associations. He also collaborates with researchers in occupational therapy, gerontology, biology, education and psychology. Wilcox is an internationally recognized expert in the field of Applied Statistics and has concentrated much of his research in the area of ANOVA and Regression. Wilcox is the author of 12 books on statistics and has published many papers on robust methods. He is currently an Associate Editor for four statistics journals and has served on many editorial boards. He has given numerous invited talks and workshops on robust methods.

Affiliations and Expertise

University of Southern California, USA