Nonparametric Statistical Methods

Praise for the Second Edition

"This book should be an essential part of the personal
library of every practicing
statistician."--Technometrics

Thoroughly revised and updated, the new edition of Nonparametric
Statistical Methods includes additional modern topics and
procedures, more practical data sets, and new problems from
real-life situations. The book continues to emphasize the
importance of nonparametric methods as a significant branch of
modern statistics and equips readers with the conceptual and
technical skills necessary to select and apply the appropriate
procedures for any given situation.

Written by leading statisticians, Nonparametric Statistical
Methods, Third Edition provides readers with crucial
nonparametric techniques in a variety of settings, emphasizing the
assumptions underlying the methods. The book provides an extensive
array of examples that clearly illustrate how to use nonparametric
approaches for handling one- or two-sample location and dispersion
problems, dichotomous data, and one-way and two-way layout
problems. In addition, the Third Edition features:

• The use of the freely available R software to aid in
  computation and simulation, including many new R programs written
  explicitly for this new edition

• New chapters that address density estimation, wavelets,
  smoothing, ranked set sampling, and Bayesian nonparametrics

• Problems that illustrate examples from agricultural science,
  astronomy, biology, criminology, education, engineering,
  environmental science, geology, home economics, medicine,
  oceanography, physics, psychology, sociology, and space
  science

Nonparametric Statistical Methods, Third Edition is an
excellent reference for applied statisticians and practitioners who
seek a review of nonparametric methods and their relevant
applications. The book is also an ideal textbook for
upper-undergraduate and first-year graduate courses in applied
nonparametric statistics.

Auteur

MYLES HOLLANDER is Robert O. Lawton Distinguished
Professor of Statistics and Professor Emeritus at the Florida State
University in Tallahassee. He served as editor of the Theory and
Methods Section of the Journal of the American Statistical
Association, 1993-96, and he received the Gottfried E.
Noether Senior Scholar Award from the American Statistical
Association in 2003.

DOUGLAS A. WOLFE is Professor and Chair Emeritus in the
Department of Statistics at Ohio State University in Columbus. He
is a two-time recipient of the Ohio State University Alumni
Distinguished Teaching Award, in 1973-74 and 1988-89.

ERIC CHICKEN is Associate Professor at the Florida State
University in Tallahassee. He is active in modern nonparametric
statistics research fields, including functional analysis,
sequential methods, and complex system applications.

Résumé

Praise for the Second Edition
This book should be an essential part of the personal library of every practicing statistician.**Technometrics

Thoroughly revised and updated, the new edition of Nonparametric Statistical Methods includes additional modern topics and procedures, more practical data sets, and new problems from real-life situations. The book continues to emphasize the importance of nonparametric methods as a significant branch of modern statistics and equips readers with the conceptual and technical skills necessary to select and apply the appropriate procedures for any given situation.

Written by leading statisticians, Nonparametric Statistical Methods, Third Edition provides readers with crucial nonparametric techniques in a variety of settings, emphasizing the assumptions underlying the methods. The book provides an extensive array of examples that clearly illustrate how to use nonparametric approaches for handling one- or two-sample location and dispersion problems, dichotomous data, and one-way and two-way layout problems. In addition, the Third Edition features:

• The use of the freely available R software to aid in computation and simulation, including many new R programs written explicitly for this new edition
• New chapters that address density estimation, wavelets, smoothing, ranked set sampling, and Bayesian nonparametrics
• Problems that illustrate examples from agricultural science, astronomy, biology, criminology, education, engineering, environmental science, geology, home economics, medicine, oceanography, physics, psychology, sociology, and space science Nonparametric Statistical Methods, Third Edition is an excellent reference for applied statisticians and practitioners who seek a review of nonparametric methods and their relevant applications. The book is also an ideal textbook for upper-undergraduate and first-year graduate courses in applied nonparametric statistics.

Contenu

Preface xiii

1. Introduction 1

1.1. Advantages of Nonparametric Methods 1

1.2. The Distribution-Free Property 2

1.3. Some Real-World Applications 3

1.4. Format and Organization 6

1.5. Computing with R 8

1.6. Historical Background 9

2. The Dichotomous Data Problem 11

Introduction 11

2.1. A Binomial Test 11

2.2. An Estimator for the Probability of Success 22

2.3. A Confidence Interval for the Probability of Success (Wilson) 24

2.4. Bayes Estimators for the Probability of Success 33

3. The One-Sample Location Problem 39

Introduction 39

Paired Replicates Analyses by Way of Signed Ranks 39

3.1. A Distribution-Free Signed Rank Test (Wilcoxon) 40

3.2. An Estimator Associated with Wilcoxon's Signed Rank Statistic (HodgesLehmann) 56

3.3. A Distribution-Free Confidence Interval Based on Wilcoxon's Signed Rank Test (Tukey) 59

Paired Replicates Analyses by Way of Signs 63

3.4. A Distribution-Free Sign Test (Fisher) 63

3.5. An Estimator Associated with the Sign Statistic (HodgesLehmann) 76

3.6. A Distribution-Free Confidence Interval Based on the Sign Test (Thompson, Savur) 80

One-Sample Data 84

3.7. Procedures Based on the Signed Rank Statistic 84

3.8. Procedures Based on the Sign Statistic 90

3.9. An Asymptotically Distribution-Free Test of Symmetry (RandlesFlignerPolicelloWolfe, DavisQuade) 94

Bivariate Data 102

3.10. A Distribution-Free Test for Bivariate Symmetry (Hollander) 102

3.11. Efficiencies of Paired Replicates and One-Sample Location Procedures 112

4. The Two-Sample Location Problem 115

Introduction 115

4.1. A Distribution-Free Rank Sum Test (Wilcoxon, Mann and Whitney) 115

4.2. An Estimator Associated with Wilcoxon's Rank Sum Statistic (HodgesLehmann) 136

4.3. A Distribution-Free Confidence Interval Based on Wilcoxon's Rank Sum Test (Moses) 142

4.4. A Robust Rank Test for the BehrensFisher Problem (FlignerPolicello) 145

4.5. Efficiencies of Two-Sample Location Procedures 149

5. The Two-Sample Dispersion Problem and Other Two-Sample Problems 151

Introduction 151

5.1. A Distribution-Free Rank Test for DispersionMedians Equal (AnsariBradley) 152

5.2. An Asymptotically Distribution-Free Test for Dispersion Based on the JackknifeMedians Not Necessarily Equal (Miller) 169

5.3. A Distribution-Free Rank Test for Either Location or Dispersion (Lepage) 181

5.4. A Distribution-Free Test for General Differences in Two Populations (KolmogorovSmirnov) 190

5.5. Efficiencies of Two-Sample Dispersion and Broad Alternatives Procedures 200

6. The One-Way Layout 202

Introduction 202

6.1. A Distribution-Free Test for General Alternatives (KruskalWallis) 204

6.2. A Distribution-Free Test for Ordered Alternatives (JonckheereTerpstra) 215

6.3. Distribution-Free Tests for Umbrella Alternatives (MackWolfe) 225

6.3A. A Distribution-Free Test for Umbrella Alternatives, Peak Known (MackWolfe) 226

6.3B. A Distribution-Free Test…