Nonparametric Statistical Methods

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.

• Preface xiii1. Introduction 11.1. Advantages of Nonparametric Methods 11.2. The Distribution-Free Property 21.3. Some Real-World Applications 31.4. Format and Organization 61.5. Computing with R 81.6. Historical Background 92. The Dichotomous Data Problem 11Introduction 112.1. A Binomial Test 112.2. An Estimator for the Probability of Success 222.3. A Confidence Interval for the Probability of Success (Wilson) 242.4. Bayes Estimators for the Probability of Success 333. The One-Sample Location Problem 39Introduction 39Paired Replicates Analyses by Way of Signed Ranks 393.1. A Distribution-Free Signed Rank Test (Wilcoxon) 403.2. An Estimator Associated with Wilcoxon’s Signed Rank Statistic (Hodges–Lehmann) 563.3. A Distribution-Free Confidence Interval Based on Wilcoxon’s Signed Rank Test (Tukey) 59Paired Replicates Analyses by Way of Signs 633.4. A Distribution-Free Sign Test (Fisher) 633.5. An Estimator Associated with the Sign Statistic (Hodges–Lehmann) 763.6. A Distribution-Free Confidence Interval Based on the Sign Test (Thompson, Savur) 80One-Sample Data 843.7. Procedures Based on the Signed Rank Statistic 843.8. Procedures Based on the Sign Statistic 903.9. An Asymptotically Distribution-Free Test of Symmetry (Randles–Fligner–Policello–Wolfe, Davis–Quade) 94Bivariate Data 1023.10. A Distribution-Free Test for Bivariate Symmetry (Hollander) 1023.11. Efficiencies of Paired Replicates and One-Sample Location Procedures 1124. The Two-Sample Location Problem 115Introduction 1154.1. A Distribution-Free Rank Sum Test (Wilcoxon, Mann and Whitney) 1154.2. An Estimator Associated with Wilcoxon’s Rank Sum Statistic (Hodges–Lehmann) 1364.3. A Distribution-Free Confidence Interval Based on Wilcoxon’s Rank Sum Test (Moses) 1424.4. A Robust Rank Test for the Behrens–Fisher Problem (Fligner–Policello) 1454.5. Efficiencies of Two-Sample Location Procedures 1495. The Two-Sample Dispersion Problem and Other Two-Sample Problems 151Introduction 1515.1. A Distribution-Free Rank Test for Dispersion–Medians Equal (Ansari–Bradley) 1525.2. An Asymptotically Distribution-Free Test for Dispersion Based on the Jackknife–Medians Not Necessarily Equal (Miller) 1695.3. A Distribution-Free Rank Test for Either Location or Dispersion (Lepage) 1815.4. A Distribution-Free Test for General Differences in Two Populations (Kolmogorov–Smirnov) 1905.5. Efficiencies of Two-Sample Dispersion and Broad Alternatives Procedures 2006. The One-Way Layout 202Introduction 2026.1. A Distribution-Free Test for General Alternatives (Kruskal–Wallis) 2046.2. A Distribution-Free Test for Ordered Alternatives (Jonckheere–Terpstra) 2156.3. Distribution-Free Tests for Umbrella Alternatives (Mack–Wolfe) 2256.3A. A Distribution-Free Test for Umbrella Alternatives, Peak Known (Mack–Wolfe) 2266.3B. A Distribution-Free Test for Umbrella Alternatives, Peak Unknown (Mack–Wolfe) 2416.4. A Distribution-Free Test for Treatments Versus a Control (Fligner–Wolfe) 249Rationale For Multiple Comparison Procedures 2556.5. Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings–General Configuration (Dwass, Steel, and Critchlow–Fligner) 2566.6. Distribution-Free One-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings-Ordered Treatment Effects (Hayter–Stone) 2656.7. Distribution-Free One-Sided Treatments-Versus-Control Multiple Comparisons Based on Joint Rankings (Nemenyi, Damico–Wolfe) 2716.8. Contrast Estimation Based on Hodges–Lehmann Two-Sample Estimators (Spjøtvoll) 2786.9. Simultaneous Confidence Intervals for All Simple Contrasts (Critchlow–Fligner) 2826.10. Efficiencies of One-Way Layout Procedures 2877. The Two-Way Layout 289Introduction 2897.1. A Distribution-Free Test for General Alternatives in a Randomized Complete Block Design (Friedman, Kendall-Babington Smith) 2927.2. A Distribution-Free Test for Ordered Alternatives in a Randomized Complete Block Design (Page) 304Rationale for Multiple Comparison Procedures 3157.3. Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Friedman Rank Sums–General Configuration (Wilcoxon, Nemenyi, McDonald-Thompson) 3167.4. Distribution-Free One-Sided Treatments Versus Control Multiple Comparisons Based on Friedman Rank Sums (Nemenyi, Wilcoxon-Wilcox, Miller) 3227.5. Contrast Estimation Based on One-Sample Median Estimators (Doksum) 328Incomplete Block Data–Two-Way Layout with Zero or One Observation Per Treatment–Block Combination 3317.6. A Distribution-Free Test for General Alternatives in a Randomized Balanced Incomplete Block Design (BIBD) (Durbin–Skillings–Mack) 3327.7. Asymptotically Distribution-Free Two-Sided All-Treatments Multiple Comparisons for Balanced Incomplete Block Designs (Skillings–Mack) 3417.8. A Distribution-Free Test for General Alternatives for Data From an Arbitrary Incomplete Block Design (Skillings–Mack) 343Replications–Two-Way Layout with at Least One Observation for Every Treatment–Block Combination 3547.9. 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) 3547.10. 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) 367Analyses Associated with Signed Ranks 3707.11. A Test Based on Wilcoxon Signed Ranks for General Alternatives in a Randomized Complete Block Design (Doksum) 3707.12. A Test Based on Wilcoxon Signed Ranks for Ordered Alternatives in a Randomized Complete Block Design (Hollander) 3767.13. Approximate Two-Sided All-Treatments Multiple Comparisons Based on Signed Ranks (Nemenyi) 3797.14. Approximate One-Sided Treatments-Versus-Control Multiple Comparisons Based on Signed Ranks (Hollander) 3827.15. Contrast Estimation Based on the One-Sample Hodges–Lehmann Estimators (Lehmann) 3867.16. Efficiencies of Two-Way Layout Procedures 3908. The Independence Problem 393Introduction 3938.1. A Distribution-Free Test for Independence Based on Signs (Kendall) 3938.2. An Estimator Associated with the Kendall Statistic (Kendall) 4138.3. An Asymptotically Distribution-Free Confidence Interval Based on the Kendall Statistic (Samara-Randles, Fligner–Rust, Noether) 4158.4. An Asymptotically Distribution-Free Confidence Interval Based on Efron’s Bootstrap 4208.5. A Distribution-Free Test for Independence Based on Ranks (Spearman) 4278.6. A Distribution-Free Test for Independence Against Broad Alternatives (Hoeffding) 4428.7. Efficiencies of Independence Procedures 4509. Regression Problems 451Introduction 451One Regression Line 4529.1. A Distribution-Free Test for the Slope of the Regression Line (Theil) 4529.2. A Slope Estimator Associated with the Theil Statistic (Theil) 4589.3. A Distribution-Free Confidence Interval Associated with the Theil Test (Theil) 4609.4. An Intercept Estimator Associated with the Theil Statistic and Use of the Estimated Linear Relationship for Prediction (Hettmansperger–McKean–Sheather) 463k(≥2) Regression Lines 4669.5. An Asymptotically Distribution-Free Test for the Parallelism of Several Regression Lines (Sen, Adichie) 466General Multiple Linear Regression 4759.6. Asymptotically Distribution-Free Rank-Based Tests for General Multiple Linear Regression (Jaeckel, Hettmansperger–McKean) 475Nonparametric Regression Analysis 4909.7. An Introduction to Non-Rank-Based Approaches to Nonparametric Regression Analysis 4909.8. Efficiencies of Regression Procedures 49410. Comparing Two Success Probabilities 495Introduction 49510.1. Approximate Tests and Confidence Intervals for the Difference between Two Success Probabilities (Pearson) 49610.2. An Exact Test for the Difference between Two Success Probabilities (Fisher) 51110.3. Inference for the Odds Ratio (Fisher, Cornfield) 51510.4. Inference for k Strata of 2 × 2 Tables (Mantel and Haenszel) 52210.5. Efficiencies 53411. Life Distributions and Survival Analysis 535Introduction 53511.1. A Test of Exponentiality Versus IFR Alternatives (Epstein) 53611.2. A Test of Exponentiality Versus NBU Alternatives (Hollander–Proschan) 54511.3. A Test of Exponentiality Versus DMRL Alternatives (Hollander–Proschan) 55511.4. A Test of Exponentiality Versus a Trend Change in Mean Residual Life (Guess–Hollander–Proschan) 56311.5. A Confidence Band for the Distribution Function (Kolmogorov) 56811.6. An Estimator of the Distribution Function When the Data are Censored (Kaplan–Meier) 57811.7. A Two-Sample Test for Censored Data (Mantel) 59411.8. Efficiencies 60512. Density Estimation 609Introduction 60912.1. Density Functions and Histograms 60912.2. Kernel Density Estimation 61712.3. Bandwidth Selection 62412.4. Other Methods 62813. Wavelets 629Introduction 62913.1. Wavelet Representation of a Function 63013.2. Wavelet Thresholding 64413.3. Other Uses of Wavelets in Statistics 65514. Smoothing 656Introduction 65614.1. Local Averaging (Friedman) 65714.2. Local Regression (Cleveland) 66214.3. Kernel Smoothing 66714.4. Other Methods of Smoothing 67515. Ranked Set Sampling 676Introduction 67615.1. Rationale and Historical Development 67615.2. Collecting a Ranked Set Sample 67715.3. Ranked Set Sampling Estimation of a Population Mean 68515.4. Ranked Set Sample Analogs of the Mann–Whitney–Wilcoxon Two-Sample Procedures (Bohn–Wolfe) 71715.5. Other Important Issues for Ranked Set Sampling 73715.6. Extensions and Related Approaches 74216. An Introduction to Bayesian Nonparametric Statistics via the Dirichlet Process 744Introduction 74416.1. Ferguson’s Dirichlet Process 74516.2. A Bayes Estimator of the Distribution Function (Ferguson) 74916.3. Rank Order Estimation (Campbell and Hollander) 75216.4. A Bayes Estimator of the Distribution When the Data are Right-Censored (Susarla and Van Ryzin) 75516.5. Other Bayesian Approaches 759Bibliography 763R Program Index 791Author Index 799Subject Index 809