Robust Nonparametric Statistical Methods: 2nd Edition (Hardback) book cover

Robust Nonparametric Statistical Methods

2nd Edition

By Thomas P. Hettmansperger, Joseph W. McKean

CRC Press

554 pages | 38 B/W Illus.

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Presenting an extensive set of tools and methods for data analysis, Robust Nonparametric Statistical Methods, Second Edition covers univariate tests and estimates with extensions to linear models, multivariate models, times series models, experimental designs, and mixed models. It follows the approach of the first edition by developing rank-based methods from the unifying theme of geometry. This edition, however, includes more models and methods and significantly extends the possible analyses based on ranks.

New to the Second Edition

  • A new section on rank procedures for nonlinear models
  • A new chapter on models with dependent error structure, covering rank methods for mixed models, general estimating equations, and time series
  • New material on the development of computationally efficient affine invariant/equivariant sign methods based on transform-retransform techniques in multivariate models

Taking a comprehensive, unified approach to statistical analysis, the book continues to describe one- and two-sample problems, the basic development of rank methods in the linear model, and fixed effects experimental designs. It also explores models with dependent error structure and multivariate models. The authors illustrate the implementation of the methods using many real-world examples and R. More information about the data sets and R packages can be found at


The coverage is expanded over the first edition to include recent developments in the field. … Hettmansperger and McKean examine a wealth of interesting problems in connection with applying nonparametric robust methods. … this is a well-written and nicely presented book that is likely to appeal to a reader with a good mathematical background and an interest in robust and nonparametric statistical methods. In my opinion, the book could provide the basis for a seminar in robust non-parametric methods for graduate students in statistics or mathematics.

—Eugenia Stoimenova, Journal of Applied Statistics, June 2012

… more logical and concise and more user-friendly … the book will be equally attractive to instructors, students, and researchers. In summary, this is a well written, structured, and presented book and offers readers plenty of examples and exercises. If I have the opportunity in the near future to offer a graduate course on robust nonparametric methods, I will definitely adopt this book with no hesitation.

Technometrics, November 2011

This book gives an excellent treatment of modern rank-based methods with a special attention to their practical application to data. … a welcome highly up-to-date and very readable contribution to the field. It will certainly become a standard reference for nonparametric and robust methods. I recommend the book as an important textbook for research libraries. The book will soon find its place on the shelves and the tables of many kind of researchers and will serve as a graduate course textbook.

—Hannu Oja, International Statistical Review (2011), 79

… a fine capstone course in non-parametric statistics.

MAA Reviews, June 2011

Table of Contents

One-Sample Problems


Location Model

Geometry and Inference in the Location Model


Properties of Norm-Based Inference

Robustness Properties of Norm-Based Inference

Inference and the Wilcoxon Signed-Rank Norm

Inference Based on General Signed-Rank Norms

Ranked Set Sampling

L1 Interpolated Confidence Intervals

Two-Sample Analysis

Two-Sample Problems


Geometric Motivation


Inference Based on the Mann-Whitney-Wilcoxon

General Rank Scores

L1 Analyses

Robustness Properties

Proportional Hazards

Two-Sample Rank Set Sampling (RSS)

Two-Sample Scale Problem

Behrens-Fisher Problem

Paired Designs

Linear Models


Geometry of Estimation and Tests


Assumptions for Asymptotic Theory

Theory of Rank-Based Estimates

Theory of Rank-Based Tests

Implementation of the R Analysis

L1 Analysis


Survival Analysis

Correlation Model

High Breakdown (HBR) Estimates

Diagnostics for Differentiating between Fits

Rank-Based Procedures for Nonlinear Models

Experimental Designs: Fixed Effects


One-Way Design

Multiple Comparison Procedures

Two-Way Crossed Factorial

Analysis of Covariance

Further Examples

Rank Transform

Models with Dependent Error Structure


General Mixed Models

Simple Mixed Models

Arnold Transformations

General Estimating Equations (GEE)

Time Series


Multivariate Location Model


Spatial Methods

Affine Equivariant and Invariant Methods

Robustness of Estimates of Location

Linear Model

Experimental Designs

Appendix: Asymptotic Results



About the Authors

Thomas P. Hettmansperger is a professor emeritus of statistics at Penn State University. Dr. Hettmansperger is a fellow of the American Statistical Association and Institute of Mathematical Statistics and an elected member of the International Statistical Institute. His research interests span nonparametric statistics, robust methods, and mixture models.

Joseph W. McKean is a professor of statistics at Western Michigan University. His research interests include robust nonparametric procedures for linear, nonlinear, and mixed models and times series designs. A fellow of the American Statistical Association, Dr. McKean has developed highly efficient and high breakdown procedures.

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General