2nd Edition

Robust Nonparametric Statistical Methods

    554 Pages 38 B/W Illustrations
    by CRC Press

    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
    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




    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 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