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 Wilcoxonâs Signed Rank Statistic (Hodgesâ"Lehmann) 56
3.3. A Distribution-Free Confidence Interval Based on Wilcoxonâs 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 (Hodgesâ"Lehmann) 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 (Randlesâ"Flignerâ"Policelloâ"Wolfe, Davisâ"Quade) 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 Wilcoxonâs Rank Sum Statistic (Hodgesâ"Lehmann) 136
4.3. A Distribution-Free Confidence Interval Based on Wilcoxonâs Rank Sum Test (Moses) 142
4.4. A Robust Rank Test for the Behrensâ"Fisher Problem (Flignerâ"Policello) 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 Dispersionâ"Medians Equal (Ansariâ"Bradley) 152
5.2. An Asymptotically Distribution-Free Test for Dispersion Based on the Jackknifeâ"Medians 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 (Kolmogorovâ"Smirnov) 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 (Kruskalâ"Wallis) 204
6.2. A Distribution-Free Test for Ordered Alternatives (Jonckheereâ"Terpstra) 215
6.3. Distribution-Free Tests for Umbrella Alternatives (Mackâ"Wolfe) 225
6.3A. A Distribution-Free Test for Umbrella Alternatives, Peak Known (Mackâ"Wolfe) 226
6.3B. A Distribution-Free Test for Umbrella Alternatives, Peak Unknown (Mackâ"Wolfe) 241
6.4. A Distribution-Free Test for Treatments Versus a Control (Flignerâ"Wolfe) 249
Rationale For Multiple Comparison Procedures 255
6.5. Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankingsâ"General Configuration (Dwass, Steel, and Critchlowâ"Fligner) 256
6.6. Distribution-Free One-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings-Ordered Treatment Effects (Hayterâ"Stone) 265
6.7. Distribution-Free One-Sided Treatments-Versus-Control Multiple Comparisons Based on Joint Rankings (Nemenyi, Damicoâ"Wolfe) 271
6.8. Contrast Estimation Based on Hodgesâ"Lehmann Two-Sample Estimators (Spj¸tvoll) 278
6.9. Simultaneous Confidence Intervals for All Simple Contrasts (Critchlowâ"Fligner) 282
6.10. Efficiencies of One-Way Layout Procedures 287
7. The Two-Way Layout 289
Introduction 289
7.1. A Distribution-Free Test for General Alternatives in a Randomized Complete Block Design (Friedman, Kendall-Babington Smith) 292
7.2. A Distribution-Free Test for Ordered Alternatives in a Randomized Complete Block Design (Page) 304
Rationale for Multiple Comparison Procedures 315
7.3. Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Friedman Rank Sumsâ"General Configuration (Wilcoxon, Nemenyi, McDonald-Thompson) 316
7.4. Distribution-Free One-Sided Treatments Versus Control Multiple Comparisons Based on Friedman Rank Sums (Nemenyi, Wilcoxon-Wilcox, Miller) 322
7.5. Contrast Estimation Based on One-Sample Median Estimators (Doksum) 328
Incomplete Block Dataâ"Two-Way Layout with Zero or One Observation Per Treatmentâ"Block Combination 331
7.6. A Distribution-Free Test for General Alternatives in a Randomized Balanced Incomplete Block Design (BIBD) (Durbinâ"Skillingsâ"Mack) 332
7.7. Asymptotically Distribution-Free Two-Sided All-Treatments Multiple Comparisons for Balanced Incomplete Block Designs (Skillingsâ"Mack) 341
7.8. A Distribution-Free Test for General Alternatives for Data From an Arbitrary Incomplete Block Design (Skillingsâ"Mack) 343
Replicationsâ"Two-Way Layout with at Least One Observation for Every Treatmentâ"Block Combination 354
7.9. A Distribution-Free Test for General Alternatives in a Randomized Block Design with an Equal Number c(>1) of Replications Per Treatmentâ"Block Combination (Mackâ"Skillings) 354
7.10. Asymptotically Distribution-Free Two-Sided All-Treatments Multiple Comparisons for a Two-Way Layout with an Equal Number of Replications in Each Treatmentâ"Block Combination (Mackâ"Skillings) 367
Analyses Associated with Signed Ranks 370
7.11. A Test Based on Wilcoxon Signed Ranks for General Alternatives in a Randomized Complete Block Design (Doksum) 370
7.12. A Test Based on Wilcoxon Signed Ranks for Ordered Alternatives in a Randomized Complete Block Design (Hollander) 376
7.13. Approximate Two-Sided All-Treatments Multiple Comparisons Based on Signed Ranks (Nemenyi) 379
7.14. Approximate One-Sided Treatments-Versus-Control Multiple Comparisons Based on Signed Ranks (Hollander) 382
7.15. Contrast Estimation Based on the One-Sample Hodgesâ"Lehmann Estimators (Lehmann) 386
7.16. Efficiencies of Two-Way Layout Procedures 390
8. The Independence Problem 393
Introduction 393
8.1. A Distribution-Free Test for Independence Based on Signs (Kendall) 393
8.2. An Estimator Associated with the Kendall Statistic (Kendall) 413
8.3. An Asymptotically Distribution-Free Confidence Interval Based on the Kendall Statistic (Samara-Randles, Flignerâ"Rust, Noether) 415
8.4. An Asymptotically Distribution-Free Confidence Interval Based on Efronâs Bootstrap 420
8.5. A Distribution-Free Test for Independence Based on Ranks (Spearman) 427
8.6. A Distribution-Free Test for Independence Against Broad Alternatives (Hoeffding) 442
8.7. Efficiencies of Independence Procedures 450
9. Regression Problems 451
Introduction 451
One Regression Line 452
9.1. A Distribution-Free Test for the Slope of the Regression Line (Theil) 452
9.2. A Slope Estimator Associated with the Theil Statistic (Theil) 458
9.3. A Distribution-Free Confidence Interval Associated with the Theil Test (Theil) 460
9.4. An Intercept Estimator Associated with the Theil Statistic and Use of the Estimated Linear Relationship for Prediction (Hettmanspergerâ"McKeanâ"Sheather) 463
k(â¥2) Regression Lines 466
9.5. An Asymptotically Distribution-Free Test for the Parallelism of Several Regression Lines (Sen, Adichie) 466
General Multiple Linear Regression 475
9.6. Asymptotically Distribution-Free Rank-Based Tests for General Multiple Linear Regression (Jaeckel, Hettmanspergerâ"McKean) 475
Nonparametric Regression Analysis 490
9.7. An Introduction to Non-Rank-Based Approaches to Nonparametric Regression Analysis 490
9.8. Efficiencies of Regression Procedures 494
10. Comparing Two Success Probabilities 495
Introduction 495
10.1. Approximate Tests and Confidence Intervals for the Difference between Two Success Probabilities (Pearson) 496
10.2. An Exact Test for the Difference between Two Success Probabilities (Fisher) 511
10.3. Inference for the Odds Ratio (Fisher, Cornfield) 515
10.4. Inference for k Strata of 2 - 2 Tables (Mantel and Haenszel) 522
10.5. Efficiencies 534
11. Life Distributions and Survival Analysis 535
Introduction 535
11.1. A Test of Exponentiality Versus IFR Alternatives (Epstein) 536
11.2. A Test of Exponentiality Versus NBU Alternatives (Hollanderâ"Proschan) 545
11.3. A Test of Exponentiality Versus DMRL Alternatives (Hollanderâ"Proschan) 555
11.4. A Test of Exponentiality Versus a Trend Change in Mean Residual Life (Guessâ"Hollanderâ"Proschan) 563
11.5. A Confidence Band for the Distribution Function (Kolmogorov) 568
11.6. An Estimator of the Distribution Function When the Data are Censored (Kaplanâ"Meier) 578
11.7. A Two-Sample Test for Censored Data (Mantel) 594
11.8. Efficiencies 605
12. Density Estimation 609
Introduction 609
12.1. Density Functions and Histograms 609
12.2. Kernel Density Estimation 617
12.3. Bandwidth Selection 624
12.4. Other Methods 628
13. Wavelets 629
Introduction 629
13.1. Wavelet Representation of a Function 630
13.2. Wavelet Thresholding 644
13.3. Other Uses of Wavelets in Statistics 655
14. Smoothing 656
Introduction 656
14.1. Local Averaging (Friedman) 657
14.2. Local Regression (Cleveland) 662
14.3. Kernel Smoothing 667
14.4. Other Methods of Smoothing 675
15. Ranked Set Sampling 676
Introduction 676
15.1. Rationale and Historical Development 676
15.2. Collecting a Ranked Set Sample 677
15.3. Ranked Set Sampling Estimation of a Population Mean 685
15.4. Ranked Set Sample Analogs of the Mannâ"Whitneyâ"Wilcoxon Two-Sample Procedures (Bohnâ"Wolfe) 717
15.5. Other Important Issues for Ranked Set Sampling 737
15.6. Extensions and Related Approaches 742
16. An Introduction to Bayesian Nonparametric Statistics via the Dirichlet Process 744
Introduction 744
16.1. Fergusonâs Dirichlet Process 745
16.2. A Bayes Estimator of the Distribution Function (Ferguson) 749
16.3. Rank Order Estimation (Campbell and Hollander) 752
16.4. A Bayes Estimator of the Distribution When the Data are Right-Censored (Susarla and Van Ryzin) 755
16.5. Other Bayesian Approaches 759
Bibliography 763
R Program Index 791
Author Index 799
Subject Index 809
