Nonparametric Statistical Methods Using R

Praise for the first edition:“This book would be especially good for the shelf of anyone who already knows nonparametrics, but wants a reference for how to apply those techniques in R.”-The American StatisticianThis thoroughly updated and expanded second edition of Nonparametric Statistical Methods Using R covers traditional nonparametric methods and rank-based analyses. Two new chapters covering multivariate analyses and big data have been added. Core classical nonparametrics chapters on one- and two-sample problems have been expanded to include discussions on ties as well as power and sample size determination. Common machine learning topics --- including k-nearest neighbors and trees --- have also been included in this new edition.Key Features: Covers a wide range of models including location, linear regression, ANOVA-type, mixed models for cluster correlated data, nonlinear, and GEE-type. Includes robust methods for linear model analyses, big data, time-to-event analyses, timeseries, and multivariate. Numerous examples illustrate the methods and their computation. R packages are available for computation and datasets. Contains two completely new chapters on big data and multivariate analysis. The book is suitable for advanced undergraduate and graduate students in statistics and data science, and students of other majors with a solid background in statistical methods including regression and ANOVA. It will also be of use to researchers working with nonparametric and rank-based methods in practice. Cover Half Title Series Page Title Page Copyright Page Dedication Contents Preface Preface from the First Edition 1. Introduction 1.1. Data and Notation 1.1.1. Data Types in R 1.1.2. Vector and Matrix Notation 1.1.3. Data Frames 1.1.4. Ranks 1.2. Graphics 1.3. Monte Carlo Simulation 1.3.1. Estimates of Center: Sample Mean and Sample Median 1.4. Functions 1.4.1. Single Line Functions 1.4.2. Level and Power of a Statistical Test 1.4.3. Functions 1.5. Randomization 1.6. Density Estimation 1.6.1. Some Details 1.7. Exercises 2. One-Sample Problems 2.1. Introduction 2.2. One-Sample Proportion Problems 2.3. Sign Test 2.3.1. Power Simulation 2.4. Signed-Rank Wilcoxon 2.4.1. Estimation and Confidence Intervals 2.4.2. Computation in R 2.4.3. Density Estimation Revisited 2.5. Adjustments for Ties 2.5.1. Sign Test 2.5.2. Signed-Rank Wilcoxon 2.6. Confidence Interval Based Estimates of Standard Errors 2.7. Asymptotic Tests 2.7.1. Signed-Rank Wilcoxon Test 2.7.2. Sign Test 2.8. Bootstrap 2.8.1. Percentile Bootstrap Confidence Intervals 2.8.2. Bootstrap Tests of Hypotheses 2.9. Robustness 2.10. Power and Sample Size Determination 2.10.1. Power of One-Sample Rank-Based Tests 2.10.2. Sample Size Determination 2.10.3. Randomized Paired Design 2.10.4. Sign Test 2.10.5. Sample Size Determination for Estimation 2.11. Exercises 3. Two-Sample Problems 3.1. Introductory Example 3.2. Rank-Based Analyses 3.2.1. Wilcoxon Test for Stochastic Ordering of Alternatives 3.2.2. Analyses for a Shift in Location 3.2.3. Analyses Based on General Score Functions 3.2.4. Linear Regression Model 3.3. Sign Scores Two-Sample Analysis 3.3.1. Mood’s Median Test 3.3.2. Estimation of the Shift in Location 3.4. Adjustments for Ties 3.5. Scale Problem 3.6. Placement Test for the Behrens–Fisher Problem 3.6.1. Estimation of a Shift Parameter, Δ 3.6.2. Classical Behrens–Fisher Model 3.7. Efficiency and Optimal Scores 3.7.1. Efficiency 3.8. Adaptive Rank Scores Tests 3.9. Power and Sample Size Determination for Rank-Based Tests 3.9.1. Power of Rank-Based Tests 3.9.2. Sample Size Determination 3.10. k-Nearest Neighbors and Cross-Validation 3.11. Kaplan–Meier and Log-Rank Test 3.11.1. Gehan’s Test 3.11.2. Composite Outcomes 3.12. Exercises 4. Regression 4.1. Introduction 4.2. Correlation 4.2.1. Pearson’s Correlation Coefficient 4.2.2. Kendall’s τK 4.2.3. Spearman’s ρS 4.2.4. Computation and Examples 4.3. Simple Linear Regression 4.4. Multiple Linear Regression 4.4.1. Multiple Regression 4.4.2. Polynomial Regression 4.5. Bootstrap 4.6. Nonparametric Regression 4.6.1. Polynomial Models 4.6.2. Nonparametric Regression 4.7. Exercises 5. ANOVA-Type Rank-Based Procedures 5.1. Introduction 5.2. One-Way ANOVA 5.2.1. Multiple Comparisons 5.2.2. Kruskal–Wallis Test 5.3. Multi-Way Crossed Factorial Design 5.3.1. Two-Way 5.3.2. k-Way 5.4. Contrasts 5.5. Additive Model 5.6. ANCOVA 5.6.1. Computation of Rank-Based ANCOVA 5.7. Ordered Alternatives 5.8. Multi-Sample Scale Problem 5.9. Exercises 6. Categorical Data 6.1. Comparison of Two Probabilities 6.1.1. Risk Difference 6.1.2. Comparison of Two Rates 6.1.3. Confidence Interval for the Risk Ratio 6.1.4. Confidence Interval for the Odds Ratio 6.2. χ2 Tests 6.2.1. Goodness-of-Fit Tests for a Single Discrete Random Variable 6.2.2. Several Discrete Random Variables 6.2.3. Independence of Two Discrete Random Variables 6.2.4. McNemar’s Test 6.3. Logistic Regression 6.4. Trees for Classification 6.4.1. Random Forest 6.5. Exercises 7. Linear Models 7.1. Linear Models 7.1.1. Estimation 7.1.2. Diagnostics 7.1.3. Inference 7.1.4. Confidence Interval for a Mean Response 7.2. Weighted Regression 7.3. ANCOVA 7.3.1. Computation of Rank-Based ANCOVA 7.4. Methodology for Type III Hypotheses Testing 7.5. Aligned Rank Tests 7.6. Exercises 8. Topics in Regression 8.1. Introduction 8.2. High Breakdown Rank-Based Fits 8.2.1. Weights for the HBR Fit 8.3. Robust Diagnostics 8.3.1. Graphics 8.3.2. Procedures for Differentiating between Robust Fits 8.3.3. Concluding Remarks 8.4. Linear Models with Skew-Normal Errors 8.4.1. Sensitivity Analysis 8.4.2. Simulation Study 8.5. Hogg-Type Adaptive Procedure 8.6. Nonlinear 8.6.1. Implementation of the Wilcoxon Nonlinear Fit 8.6.2. R Computation of Rank-Based Nonlinear Fits 8.6.3. Examples 8.6.4. High Breakdown Rank-Based Fits 8.7. Time Series 8.7.1. Order of the Autoregressive Series 8.8. Cox Proportional Hazards Models 8.9. Accelerated Failure Time Models 8.10. Trees for Regression 8.11. Exercises 9. Cluster Correlated Data 9.1. Introduction 9.2. Friedman’s Test 9.3. Joint Rankings Estimator 9.3.1. Estimates of Standard Error 9.3.2. Inference 9.3.3. Examples 9.4. Robust Variance Component Estimators 9.5. Multiple Rankings Estimator 9.6. GEE-Type Estimator 9.6.1. Weights 9.6.2. Link Function 9.6.3. Working Covariance Matrix 9.6.4. Standard Errors 9.6.5. Examples 9.7. Exercises 10. Multivariate Analysis 10.1. Introduction 10.2. Brief Review of Multivariate Distributions 10.2.1. Continuous Multivariate Distributions 10.2.2. Expectation and Covariance 10.2.3. Multivariate Normal Distribution 10.3. Estimation in Multivariate Location Models 10.3.1. Multivariate Location Model 10.3.2. Estimation and Confidence Intervals 10.3.3. Median Rank-Based Estimation of θ and Confidence Intervals 10.3.4. Wilcoxon Rank-Based Estimation of θ and Confidence Intervals 10.4. Tests of Hypothesis for the Multivariate Location Model 10.4.1. Traditional Procedures 10.4.2. Contrasts 10.4.3. Robust Procedures 10.5. Multivariate Linear Models 10.5.1. Asymptotic Distribution of β 10.5.2. General Linear Hypotheses 10.6. One-Way Rank-Based MANOVA 10.7. Two-Way Rank-Based MANOVA 10.8. Exercises 11. Big Data 11.1. Approximate Scores 11.1.1. Asymptotic Distribution 11.1.2. Estimation of Scale Parameters for Big Data 11.1.3. Efficiency Based on the Number of Bins 11.1.4. Big Rfit Algorithm 11.1.5. Examples 11.2. Big Data Packages 11.2.1. data.table::fread, fwrite 11.2.2. biglm 11.2.3. Computation of Step Scores via data.table 11.3. bigRreg 11.3.1. Approximation of τ 11.4. Spark Basics 11.4.1. dbplot 11.4.2. Machine Learning Tools 11.4.3. spark disconnect 11.5. One-step Wilcoxon Estimate Using sparklyr 11.6. Exercises Appendix - R Version Information Bibliography Index