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Nonparametric Statistical Methods, 3rd Edition

Book Description

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.

    Table of Contents

    1. Cover
    2. Series
    3. Title Page
    4. Copyright
    5. Dedication
    6. Chapter 1: Introduction
      1. 1.1 Advantages of Nonparametric Methods
      2. 1.2 The Distribution-Free Property
      3. 1.3 Some Real-World Applications
      4. 1.4 Format and Organization
      5. 1.5 Computing With R
      6. 1.6 Historical Background
    7. Chapter 2: The Dichotomous Data Problem
      1. Introduction
      2. 2.1 A Binomial Test
      3. 2.2 An Estimator for The Probability of Success
      4. 2.3 A Confidence Interval for the Probability of Success (Wilson)
      5. 2.4 Bayes Estimators for the Probability of Success
    8. Chapter 3: The One-Sample Location Problem
      1. Introduction
      2. Paired Replicates Analyses by Way of Signed Ranks
      3. 3.1 A Distribution-Free Signed Rank Test (WILCOXON)
      4. 3.2 An Estimator Associated With Wilcoxon's Signed Rank Statistic (Hodges–Lehmann)
      5. 3.3 A Distribution-Free Confidence Interval Based on Wilcoxon's Signed Rank Test (TUKEY)
      6. Paired Replicates Analyses by Way of Signs
      7. 3.4 A Distribution-Free Sign Test (Fisher)
      8. 3.5 An Estimator Associated with The Sign Statistic (Hodges–Lehmann)
      9. 3.6 A Distribution-Free Confidence Interval Based on the Sign Test (Thompson, Savur)
      10. One-Sample Data*
      11. 3.7 Procedures Based on the Signed Rank Statistic
      12. 3.8 Procedures Based on the Sign Statistic
      13. 3.9 An Asymptotically Distribution-Free Test of Symmetry (Randles–Fligner– Policello–Wolfe, Davis–Quade)
      14. Bivariate Data
      15. 3.10 A Distribution-Free Test for Bivariate Symmetry (Hollander)
      16. Hypothesis
      17. 3.11 Efficiencies of Paired Replicates and One-Sample Location Procedures
    9. Chapter 4: The Two-Sample Location Problem
      1. Introduction
      2. 4.1 A Distribution-Free Rank Sum Test (Wilcoxon, Mann and Whitney)
      3. 4.2 An Estimator Associated with Wilcoxon's Rank Sum Statistic (Hodges–Lehmann)
      4. 4.3 A Distribution-Free Confidence Interval Based on Wilcoxon's Rank Sum Test (Moses)
      5. 4.4 A Robust Rank Test for the Behrens–Fisher Problem (Fligner–Policello)
      6. 4.5 Efficiencies of Two-Sample Location Procedures
    10. Chapter 5: The Two-Sample Dispersion Problem and Other Two-Sample Problems
      1. Introduction
      2. 5.1 A Distribution-Free Rank Test for Dispersion—Medians Equal (Ansari–Bradley)
      3. 5.2 An Asymptotically Distribution-Free Test for Dispersion Based on the Jackknife–Medians not Necessarily Equal (Miller)
      4. 5.3 A Distribution-Free Rank Test for Either Location or Dispersion (Lepage)
      5. 5.4 A Distribution-Free Test for General Differences in Two Populations (Kolmogorov–Smirnov)
      6. 5.5 Efficiencies of Two-Sample Dispersion and Broad Alternatives Procedures
    11. Chapter 6: The One-Way Layout
      1. Introduction
      2. 6.1 A Distribution-Free Test for General Alternatives (Kruskal–Wallis)
      3. 6.2 A Distribution-Free Test for Ordered Alternatives (Jonckheere–Terpstra)
      4. 6.3 Distribution-Free Tests for Umbrella Alternatives (Mack–Wolfe)
      5. 6.3A A Distribution-Free Test for Umbrella Alternatives, Peak Known (Mack–Wolfe)
      6. 6.3B A Distribution-Free Test for Umbrella Alternatives, Peak Unknown (Mack–Wolfe)
      7. 6.4 A Distribution-Free Test for Treatments Versus a Control (Fligner–Wolfe)
      8. Rationale For Multiple Comparison Procedures
      9. 6.5 Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings—General Configuration (Dwass, Steel, and Critchlow–Fligner)
      10. 6.6 Distribution-Free One-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings-Ordered Treatment Effects (Hayter–Stone)
      11. 6.7 Distribution-Free One-Sided Treatments- Versus-Control Multiple Comparisons Based on Joint Rankings (Nemenyi, Damico–Wolfe)
      12. 6.8 Contrast Estimation Based on Hodges–Lehmann Two-Sample Estimators (Spjøtvoll)
      13. 6.9 Simultaneous Confidence Intervals for All Simple Contrasts (Critchlow–Fligner)
      14. 6.10 Efficiencies of One-Way Layout Procedures
    12. Chapter 7: The Two-Way Layout
      1. Introduction
      2. 7.1 A Distribution-Free Test For General Alternatives In A Randomized Complete Block Design (Friedman, Kendall-Babington Smith)
      3. 7.2 A Distribution-Free Test for Ordered Alternatives in a Randomized Complete Block Design (Page)
      4. Rationale for Multiple Comparison Procedures
      5. 7.3 Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Friedman Rank Sums—General Configuration (Wilcoxon, Nemenyi, Mcdonald-Thompson)
      6. 7.4 Distribution-Free One-Sided Treatments Versus Control Multiple Comparisons Based On Friedman Rank Sums (Nemenyi, Wilcoxon–Wilcox, Miller)
      7. 7.5 Contrast Estimation Based on One-Sample Median Estimators (Doksum)
      8. Incomplete Block Data—Two-Way Layout With Zero or One Observation Per Treatment–Block Combination
      9. 7.6 A Distribution-Free Test for General Alternatives In a Randomized Balanced Incomplete Block Design (Bibd) (Durbin–Skillings–Mack)
      10. 7.7 Asymptotically Distribution-Free Two-Sided All-Treatments Multiple Comparisons for Balanced Incomplete Block Designs (Skillings–Mack)
      11. 7.8 A Distribution-Free Test for General Alternatives for Data From an Arbitrary Incomplete Block Design (Skillings–Mack)
      12. Replications—Two-Way Layout With at Least One Observation for Every Treatment–Block Combination
      13. 7.9 A Distribution-Free Test for General Alternatives In a Randomized Block Design With an Equal Number c(>1) of Replications Per Treatment–Block Combination (Mack–Skillings)
      14. 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)
      15. Analyses Associated With Signed Ranks
      16. 7.11 A Test Based on Wilcoxon Signed Ranks for General Alternatives in A Randomized Complete Block Design (Doksum)
      17. 7.12 A Test Based on Wilcoxon Signed Ranks for Ordered Alternatives in a Randomized Complete Block Design (Hollander)
      18. 7.13 Approximate Two-Sided All-Treatments Multiple Comparisons Based on Signed Ranks (Nemenyi)
      19. 7.14 Approximate One-Sided Treatments-Versus-Control Multiple Comparisons Based On Signed Ranks (Hollander)
      20. 7.15 Contrast Estimation Based on the One-Sample Hodges–Lehmann Estimators (Lehmann)
      21. 7.16 Efficiencies of Two-Way Layout Procedures
    13. Chapter 8: The Independence Problem
      1. Introduction
      2. 8.1 A Distribution-Free Test for Independence Based on Signs (Kendall)
      3. 8.2 An Estimator Associated With The Kendall Statistic (Kendall)
      4. 8.3 An Asymptotically Distribution–Free Confidence Interval Based On The Kendall Statistic (Samara–Randles, Fligner–Rust, Noether)
      5. 8.4 An Asymptotically Distribution-Free Confidence Interval Based On Efron's Bootstrap
      6. 8.5 A Distribution-Free Test for Independence Based on Ranks (Spearman)
      7. 8.6 A Distribution-Free Test for Independence Against Broad Alternatives (Hoeffding)
      8. 8.7 Efficiencies of Independence Procedures
    14. Chapter 9: Regression Problems
      1. Introduction
      2. One Regression Line
      3. 9.1 A Distribution-Free Test for the Slope of the Regression Line (Theil)
      4. 9.2 A Slope Estimator Associated with the Theil Statistic (Theil)
      5. 9.3 A Distribution-Free Confidence Interval Associated with the Theil Test (Theil)
      6. 9.4 An Intercept Estimator Associated with the Theil Statistic and Use of the Estimated Linear Relationship for Prediction (Hettmansperger–Mckean–Sheather)
      7. k(≥2) Regression Lines
      8. 9.5 An Asymptotically Distribution-Free Test for the Parallelism of Several Regression Lines (Sen, Adichie)
      9. General Multiple Linear Regression
      10. 9.6 Asymptotically Distribution-Free Rank-Based Tests for General Multiple Linear Regression (Jaeckel, Hettmansperger–Mckean)
      11. Nonparametric Regression Analysis
      12. 9.7 An Introduction to Non-Rank-Based Approaches to Nonparametric Regression Analysis
      13. 9.8 Efficiencies of Regression Procedures
    15. Chapter 10: Comparing Two Success Probabilities
      1. Introduction
      2. 10.1 Approximate Tests and Confidence Intervals for The Difference Between Two Success Probabilities (Pearson)
      3. 10.2 An Exact Test for the Difference Between Two Success Probabilities (Fisher)
      4. 10.3 Inference for the Odds Ratio (Fisher, Cornfield)
      5. 10.4 Inference for k Strata of 2×2 Tables (Mantel and Haenszel)
      6. 10.5 Efficiencies
    16. Chapter 11: Life Distributions and Survival Analysis
      1. Introduction
      2. 11.1 A Test of Exponentiality Versus IFR Alternatives (Epstein)
      3. 11.2 A Test of Exponentiality Versus NBU Alternatives (Hollander–Proschan)
      4. 11.3 A Test of Exponentiality Versus DMRL Alternatives (Hollander–Proschan)
      5. 11.4 A Test of Exponentiality Versus a Trend Change in Mean Residual Life (Guess–Hollander–Proschan)
      6. 11.5 A Confidence Band for the Distribution Function (Kolmogorov)
      7. 11.6 An Estimator of the Distribution Function When the Data are Censored (Kaplan–Meier)
      8. 11.7 A Two-Sample Test for Censored Data (Mantel)
      9. 11.8 Efficiencies
    17. Chapter 12: Density Estimation
      1. Introduction
      2. 12.1 Density Functions and Histograms
      3. 12.2 Kernel Density Estimation
      4. 12.3 Bandwidth Selection
      5. 12.4 Other Methods
    18. Chapter 13: Wavelets
      1. Introduction
      2. 13.1 Wavelet Representation of a Function
      3. 13.2 Wavelet Thresholding
      4. 13.3 Other Uses of Wavelets in Statistics
    19. Chapter 14: Smoothing
      1. Introduction
      2. 14.1 Local Averaging (Friedman)
      3. 14.2 Local Regression (Cleveland)
      4. 14.3 Kernel Smoothing
      5. 14.4 Other Methods of Smoothing
    20. Chapter 15: Ranked Set Sampling
      1. Introduction
      2. 15.1 Rationale and Historical Development
      3. 15.2 Collecting a Ranked Set Sample
      4. 15.3 Ranked Set Sampling Estimation of a Population Mean
      5. 15.4 Ranked Set Sample Analogs of the Mann–Whitney–Wilcoxon Two-Sample Procedures (Bohn–Wolfe)
      6. 15.5 Other Important Issues for Ranked Set Sampling
      7. 15.6 Extensions and Related Approaches
    21. Chapter 16: An Introduction to Bayesian Nonparametric Statistics via the Dirichlet Process
      1. Introduction
      2. 16.1 Ferguson's Dirichlet Process
      3. 16.2 A Bayes Estimator of the Distribution Function (Ferguson)
      4. 16.3 Rank Order Estimation (Campbell and Hollander)
      5. 16.4 A Bayes Estimator of the Distribution When the Data Are Right-Censored (Susarla and Van Ryzin)
      6. 16.5 Other Bayesian Approaches
    22. Bibliography
    23. R Program Index
    24. Author Index
    25. Subject Index
    26. Series