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Nonparametric Statistical Methods Using R, 2nd Edition

Name: Nonparametric Statistical Methods Using R, 2nd Edition
ISBN: 9781040025178

by John Kloke, Joseph McKean

May 2024

Intermediate to advanced

480 pages

12h 1m

English

Chapman and Hall/CRC

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Cover Page
Half-Title Page
Series Page
Title Page
Copyright Page
Dedication Page
Contents
Preface
Preface from the First Edition
1 Introduction
1.1 Data and Notation1.1.1 Data Types in R1.1.2 Vector and Matrix Notation1.1.3 Data Frames1.1.4 Ranks1.2 Graphics1.3 Monte Carlo Simulation1.3.1 Estimates of Center: Sample Mean and Sample Median1.4 Functions1.4.1 Single Line Functions1.4.2 Level and Power of a Statistical Test1.4.3 Functions1.5 Randomization1.6 Density Estimation1.6.1 Some Details1.7 Exercises

2 One-Sample Problems
2.1 Introduction2.2 One-Sample Proportion Problems2.3 Sign Test2.3.1 Power Simulation2.4 Signed-Rank Wilcoxon2.4.1 Estimation and Confidence Intervals2.4.2 Computation in R2.4.3 Density Estimation Revisited2.5 Adjustments for Ties2.5.1 Sign Test2.5.2 Signed-Rank Wilcoxon2.6 Confidence Interval Based Estimates of Standard Errors2.7 Asymptotic Tests2.7.1 Signed-Rank Wilcoxon Test2.7.2 Sign Test2.8 Bootstrap2.8.1 Percentile Bootstrap Confidence Intervals2.8.2 Bootstrap Tests of Hypotheses2.9 Robustness2.10 Power and Sample Size Determination2.10.1 Power of One-Sample Rank-Based Tests2.10.2 Sample Size Determination2.10.3 Randomized Paired Design2.10.4 Sign Test2.10.5 Sample Size Determination for Estimation2.11 Exercises
3 Two-Sample Problems
3.1 Introductory Example3.2 Rank-Based Analyses3.2.1 Wilcoxon Test for Stochastic Ordering of Alternatives3.2.2 Analyses for a Shift in Location3.2.3 Analyses Based on General Score Functions3.2.4 Linear Regression Model3.3 Sign Scores Two-Sample Analysis3.3.1 Mood's Median Test3.3.2 Estimation of the Shift in Location3.4 Adjustments for Ties3.5 Scale Problem3.6 Placement Test for the Behrens–Fisher Problem3.6.1 Estimation of a Shift Parameter, Δ3.6.2 Classical Behrens–Fisher Model3.7 Efficiency and Optimal Scores3.7.1 Efficiency3.8 Adaptive Rank Scores Tests3.9 Power and Sample Size Determination for Rank-Based Tests3.9.1 Power of Rank-Based Tests3.9.2 Sample Size Determination3.10 k-Nearest Neighbors and Cross-Validation3.11 Kaplan–Meier and Log-Rank Test3.11.1 Gehan's Test3.11.2 Composite Outcomes3.12 Exercises
4 Regression
4.1 Introduction4.2 Correlation4.2.1 Pearson's Correlation Coefficient4.2.2 Kendall's τK4.2.3 Spearman's ρS4.2.4 Computation and Examples4.3 Simple Linear Regression4.4 Multiple Linear Regression4.4.1 Multiple Regression4.4.2 Polynomial Regression4.5 Bootstrap4.6 Nonparametric Regression4.6.1 Polynomial Models4.6.2 Nonparametric Regression4.7 Exercises
5 ANOVA-Type Rank-Based Procedures
5.1 Introduction5.2 One-Way ANOVA5.2.1 Multiple Comparisons5.2.2 Kruskal–Wallis Test5.3 Multi-Way Crossed Factorial Design5.3.1 Two-Way5.3.2 k-Way5.4 Contrasts5.5 Additive Model5.6 ANCOVA5.6.1 Computation of Rank-Based ANCOVA5.7 Ordered Alternatives5.8 Multi-Sample Scale Problem5.9 Exercises
6 Categorical Data
6.1 Comparison of Two Probabilities6.1.1 Risk Difference6.1.2 Comparison of Two Rates6.1.3 Confidence Interval for the Risk Ratio6.1.4 Confidence Interval for the Odds Ratio6.2 χ2 Tests6.2.1 Goodness-of-Fit Tests for a Single Discrete Random Variable6.2.2 Several Discrete Random Variables6.2.3 Independence of Two Discrete Random Variables6.2.4 McNemar's Test6.3 Logistic Regression6.4 Trees for Classification6.4.1 Random Forest6.5 Exercises
7 Linear Models
7.1 Linear Models7.1.1 Estimation7.1.2 Diagnostics7.1.3 Inference7.1.4 Confidence Interval for a Mean Response7.2 Weighted Regression7.3 ANCOVA7.3.1 Computation of Rank-Based ANCOVA7.4 Methodology for Type III Hypotheses Testing7.5 Aligned Rank Tests7.6 Exercises
8 Topics in Regression
8.1 Introduction8.2 High Breakdown Rank-Based Fits8.2.1 Weights for the HBR Fit8.3 Robust Diagnostics8.3.1 Graphics8.3.2 Procedures for Differentiating between Robust Fits8.3.3 Concluding Remarks8.4 Linear Models with Skew-Normal Errors8.4.1 Sensitivity Analysis8.4.2 Simulation Study8.5 Hogg-Type Adaptive Procedure8.6 Nonlinear8.6.1 Implementation of the Wilcoxon Nonlinear Fit8.6.2 R Computation of Rank-Based Nonlinear Fits8.6.3 Examples8.6.4 High Breakdown Rank-Based Fits8.7 Time Series8.7.1 Order of the Autoregressive Series8.8 Cox Proportional Hazards Models8.9 Accelerated Failure Time Models8.10 Trees for Regression8.11 Exercises
9 Cluster Correlated Data
9.1 Introduction9.2 Friedman's Test9.3 Joint Rankings Estimator9.3.1 Estimates of Standard Error9.3.2 Inference9.3.3 Examples9.4 Robust Variance Component Estimators9.5 Multiple Rankings Estimator9.6 GEE-Type Estimator9.6.1 Weights9.6.2 Link Function9.6.3 Working Covariance Matrix9.6.4 Standard Errors9.6.5 Examples9.7 Exercises
10 Multivariate Analysis
10.1 Introduction10.2 Brief Review of Multivariate Distributions10.2.1 Continuous Multivariate Distributions10.2.2 Expectation and Covariance10.2.3 Multivariate Normal Distribution10.3 Estimation in Multivariate Location Models10.3.1 Multivariate Location Model10.3.2 Estimation and Confidence Intervals10.3.3 Median Rank-Based Estimation of θ and Confidence X Intervals10.3.4 Wilcoxon Rank-Based Estimation of θ and Confidence Intervals10.4 Tests of Hypothesis for the Multivariate Location Model10.4.1 Traditional Procedures10.4.2 Contrasts10.4.3 Robust Procedures10.5 Multivariate Linear Models10.5.1 Asymptotic Distribution of β^10.5.2 General Linear Hypotheses10.6 One-Way Rank-Based MANOVA10.7 Two-Way Rank-Based MANOVA10.8 Exercises
11 Big Data
11.1 Approximate Scores11.1.1 Asymptotic Distribution11.1.2 Estimation of Scale Parameters for Big Data11.1.3 Efficiency Based on the Number of Bins11.1.4 Big Rfit Algorithm11.1.5 Examples11.2 Big Data Packages11.2.1 data.table::fread, fwrite11.2.2 biglm11.2.3 Computation of Step Scores via data.table11.3 bigRreg11.3.1 Approximation of τ11.4 Spark Basics11.4.1 dbplot11.4.2 Machine Learning Tools11.4.3 spark_disconnect11.5 One-step Wilcoxon Estimate Using sparklyr11.6 Exercises
Appendix - R Version Information
Bibliography
Index

Content preview from Nonparametric Statistical Methods Using R, 2nd Edition

3Two-Sample Problems

In this chapter, we consider two-sample problems. These are simple but often used models in practice. Even in more complicated designs, contrasts of interest often involve two levels. So the ideas discussed here carry over to these designs.

In Sections 3.1–3.2, we discuss the two-sample Wilcoxon procedure. This includes the usual distribution-free rank test as well as the associated rank-based estimation, standard errors of estimates, and confidence intervals for the shift in locations. Wilcoxon procedures are based on the linear score function. Section 3.2.2.1 discusses rank-based procedures based on normal scores which are optimal if the underlying populations have normally distributed errors. We extend this discussion ...

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Nonparametric Statistical Methods Using R, 2nd Edition

by John Kloke, Joseph McKean

3Two-Sample Problems

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.