Nonparametric Statistical Methods

by Hollander, Myles; Wolfe, Douglas A.; Chicken, Eric

• ISBN13: 9780470387375
• ISBN10: 0470387378
• Edition: 3rd
• Format: Hardcover
• Copyright: 2013-12-04
• Publisher: Wiley

Summary

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. 

Author Biography

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.

Table of Contents

Preface

1 Introduction

1.1 Advantages of Nonparametric Methods

1.2 The Distribution-Free Property

1.3 Some Real-World Applications

1.4 Format and Organization

1.5 Computing with R

1.6 Historical Background

2 The Dichotomous Data Problem

2.1 A Binomial Test

2.2 An Estimator of the Probability of Success

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

2.4 Bayes Estimators for the Probability of Success

3 The One-Sample Location Problem

Paired Replicates Analyses By Way of Signed Ranks

3.1 A Distribution-Free Signed Rank Test (Wilcoxon)

3.2 An Estimator Associated with Wilcoxon's Signed Rank Statistic (Hodges-Lehmann)

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

Paired Replicate Analyses By Way of Signs

3.4 A Distribution-Free Sign Test (Fisher)

3.5 An Estimator-Associated with the Sign Statistic (Hodges-Lehmann)

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

One-Sample Data

3.7 Procedures Based on the Signed Rank Statistic

3.8 Procedures Based on the Sign Statistic

3.9 An Asymptotically Distribution-Free Test of Symmetry (Randles-Fligner-Policello-Wolfe, Davis-Quade)

Bivariate Data

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

3.11 Efficiencies of Paired Replicates and One-Sample Location Procedures

4 The Two-Sample Location Problem

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

4.2 An Estimator Associated with Wilcoxon's Rank Sum Statistic (Hodges-Lehmann)

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

4.4 A Robust Rank Test for the Behrens-Fisher Problem (Fligner-Policello)

4.5 Efficiencies of Two-Sample Location Procedures

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

5.1 A Distribution-Free Rank Test for Dispersion -- Medians Equal (Ansari-Bradley)

5.2 An Asymptotically Distribution-Free Test for Dispersion Based on the Jack-knife -- Medians Not Necessarily Equal (Miller)

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

5.4 A Distribution-Free Test for General Differences in Two Populations (Kolmogorov-Smirnov)

5.5 Efficiencies of Two-Sample Dispersion and Broad Alternatives Procedures

6 The One-Way Layout

6.1 A Distribution-Free Test for General Alternatives (Kruskal-Wallis)

6.2 A Distribution-Free Test for Ordered Alternatives (Jonckheere, Terpstra)

6.3 Distribution-Free Tests for Umbrella Alternatives (Mack-Wolfe)

6.4 A Distribution-Free Test for Treatments versus a Control (Fligner-Wolfe)

6.5 Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings--General Configuration (Dwass, Steel, Critchlow-Fligner)

6.6 Distribution-Free One-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings--Ordered Treatment Effects (Hayter-Stone)

6.7 Distribution-Free One-Sided Treatments versus Control Multiple Comparisons Based on Joint Rankings (Nemenyi, Damico-Wolfe)

6.8 Contrast Estimation Based on Hodges-Lehmann Two-Sample Estimators (Spjøtvoll)

6.9 Simultaneous Confidence Intervals for All Simple Contrasts (Critchlow-Fligner)

6.10 Efficiencies of One-Way Layout Procedures

7 The Two-Way Layout

7.1 A Distribution-Free Test for General Alternatives in a Randomized Complete Block Design (Friedman, Kendall-Babington Smith)

7.2 A Distribution-Free Test for Ordered Alternatives in a Randomized Complete Block Design (Page)

7.3 Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Friedman Rank Sums--Geeneral Configuration (Wilcoxon, Nemenyi, McDonald-Thompson)

7.4 Distribution-Free One-Sided Treatments versus Control Multiple Comparisons Based on Friedman Rank Sums (Nemenyi, Wilcoxon-Wilcox, Miller)

7.5 Contrast Estimation Based on One-Sample Median Estimators (Doksum)
Incomplete Block Data--Two-way Layout with Zero or One Observation per Treatment-Block Combination

7.6 A Distribution-Free Test for General Alternatives in a Randomized Balanced Incomplete Block Design (BIBD)(Durbin, Skillings-Mack)

7.7 Asymptotically Distribution-Free Two-Sided All Treatments Multiple Comparisons for Balanced Incomplete Block Designs (Skillings-Mack)

7.8 A Distribution-Free Test for General Alternatives for Data from an Arbitrary Incomplete Block Design (Skillings-Mack)

Replications--Two-way Layout with at Least One Observation for Every Treatment-Block Combination

7.9 A Distribution-Free Test for General Alternatives in a Randomized Block Design with an Equal Number c(> 1) of Replications in Each Treatment-Block Combination(Mack-Skillings)

7.10 Asymptotically Distribution-Free Two-Sided All-Treatments Multiple Comparisons for a Two-Way Layout with an Equal Number of Replications in Each Treatment-Block Combination (Mack-Skillings) Analyses Associated with Signed Ranks

7.11 A Test Based on Wilcoxon Signed Ranks for General Alternatives in a Randomized Complete Block Design (Doksum)

7.12 A Test Based on Wilcoxon Signed Ranks for Ordered Alternatives in a Randomized Complete Block Design (Hollander)

7.13 Approximate Two-Sided All-Treatments Multiple Comparisons Based on Signed Ranks (Nemenyi)

7.14 Approximate One-Sided Treatments versus Control Multiple Comparisons Based on Signed Ranks (Hollander)

7.15 Contrast Estimation Based on One-Sample Hodges-Lehmann Estimators (Lehmann)

7.16 Efficiencies of Two-Way Layout Procedures

8 The Independence Problem

8.1 A Distribution-Free Test for Independence Based on Signs (Kendall)

8.2 An Estimator Associated with the Kendall Statistic (Kendall)

8.3 An Asymptotically Distribution-Free Confidence Interval Based on the Kendall Statistic (Samara-Randles, Fligner-Rust, Noether)

8.4 An Asymptotically Distribution-Free Confidence Interval Based on Efron's Bootstrap

8.5 A Distribution-Free Test for Independence Based on Ranks (Spearman)

8.6 A Distribution-Free Test for Independence Against Broad Alternatives (Hoeffding)

8.7 Efficiencies of Independence Procedures

9 Regression Problems

One Regression Line

9.1 A Distribution-Free Test for the Slope of the Regression Line (Theil)

9.2 A Slope Estimator Associated with the Theil Statistic (Theil)

9.3 A Distribution-Free Confidence Interval Associated with the Theil Test (Theil)

9.4 An Intercept Estimator Associated with the Theil Statistic and Use of the Estimated Linear Relationship for Prediction (Hettmansperger-McKean-Sheather)
k(≥2) Regression Lines

9.5 An Asymptotically Distribution-Free Test for the Parallelism of Several Regression Lines (Sen, Adichie)

General Multiple Linear Regression

9.6 Asymptotically Distribution-Free Rank-Based Tests for General Multiple Linear Regression (Jaeckel, Hettmansperger-McKean)

Nonparametric Regression Analysis

9.7 An Introduction to Non-Rank-Based Approaches to Nonparametric Regression Analysis

9.8 Efficiencies of Regression Procedures

10 Comparing Two Success Probabilities

10.1 Approximate Tests and Confidence Intervals for the Difference between Two Success Probabilities (Pearson)

10.2 An Exact Test for the Difference between Two Success Probabilities (Fisher)

10.3 Inference for the Odds Ratio (Fisher, Cornfield)

10.4 Inference for k Strata of 2 x 2 Tables (Mantel and Haenzel)

10.5 Efficiencies

11 Life Distributions and Survival Analysis

11.1 A Test of Exponentiality versus IFR Alternatives (Epstein)

11.2 A Test of Exponentiality versus NBU Alternatives (Hollander-Proschan)

11.3 A Test of Exponentiality versus DMRL Alternatives (Hollander-Proschan)

11.4 A Test of Exponentiality versus a Trend Change in Mean Residual Life (Guess-Hollander-Proschan)

11.5 A Confidence Band for the Distribution Function (Kolmogorov)

11.6 An Estimator of the Distribution Function When the Data Are Censored (Kaplan-Meier)

11.7 A Two-Sample Test for Censored Data (Mantel)

11.8 Efficiencies

12 Density Estimation

12.1 Density Functions and Histograms

12.2 Kernel Density Estimation

12.3 Bandwidth Selection

12.4 Other Methods

13 Wavelets

13.1 Wavelet Representation of a Function

13.2 Wavelet Thresholding

14 Smoothing

14.1 Local Averaging (Friedman)

14.2 Local Regression (Cleveland)

14.3 Kernel Smoothing

14.4 Other Methods of Smoothing

15 Ranked Set Sampling

15.1 Rationale and Historical Development

15.2 Collecting a Ranked Set Sample

15.3 Ranked Set Sampling Estimation of a Population Mean

15.4 Ranked Set Sample Analogues of the Mann-Whitney-Wilcoxon Two-Sample Procedures (Bohn-Wolfe)

15.5 Other Important Issues for Ranked Set Sampling

15.6 Extensions and Related Results

16 An Introduction to Bayesian Nonparametric Statistics via the Dirichlet Process

16.1 Ferguson's Dirichlet Process

16.2 A Bayes Estimator of the Distribution Function (Ferguson)

16.3 Rank Order Estimation (Campbell-Hollander)

16.4 A Bayes Estimator of the Distribution when the Data are Right-Censored (Susarla and van Ryzin)

16.5 Other Bayesian Approaches

Bibliography

R Program Index

Author Index

Subject Index