2nd Edition
Robust Nonparametric Statistical Methods
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 www.crcpress.com
One-Sample Problems
Introduction
Location Model
Geometry and Inference in the Location Model
Examples
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
Introduction
Geometric Motivation
Examples
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
Introduction
Geometry of Estimation and Tests
Examples
Assumptions for Asymptotic Theory
Theory of Rank-Based Estimates
Theory of Rank-Based Tests
Implementation of the R Analysis
L1 Analysis
Diagnostics
Survival Analysis
Correlation Model
High Breakdown (HBR) Estimates
Diagnostics for Differentiating between Fits
Rank-Based Procedures for Nonlinear Models
Experimental Designs: Fixed Effects
Introduction
One-Way Design
Multiple Comparison Procedures
Two-Way Crossed Factorial
Analysis of Covariance
Further Examples
Rank Transform
Models with Dependent Error Structure
Introduction
General Mixed Models
Simple Mixed Models
Arnold Transformations
General Estimating Equations (GEE)
Time Series
Multivariate
Multivariate Location Model
Componentwise
Spatial Methods
Affine Equivariant and Invariant Methods
Robustness of Estimates of Location
Linear Model
Experimental Designs
Appendix: Asymptotic Results
References
Index
Biography
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.
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 2011This 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
