Nonparametric Statistical Methods Using R

Nonparametric Statistical Methods Using R

by John Kloke, Joseph McKean
Released October 2014
Publisher(s): Chapman and Hall/CRC
ISBN: 9781498787277

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Book description

This book covers traditional nonparametric methods and rank-based analyses, including estimation and inference for models ranging from simple location models to general linear and nonlinear models for uncorrelated and correlated responses. The authors emphasize applications and statistical computation. They illustrate the methods with many real and simulated data examples using R, including the packages Rfit and npsm, which are available on CRAN. Each chapter includes exercises, making the book suitable for an undergraduate or graduate course.

Table of contents

  1. Preliminaries
  2. Preface
  3. Chapter 1 Getting Started with R
    1. 1.1 R Basics
      1. 1.1.1 Data Frames and Matrices
    2. 1.2 Reading External Data
    3. 1.3 Generating Random Data
    4. 1.4 Graphics
    5. 1.5 Repeating Tasks
    6. 1.6 User Defined Functions
    7. 1.7 Monte Carlo Simulation
    8. 1.8 R packages
    9. 1.9 Exercises
      1. Figure 1.1
      2. Figure 1.2
  4. Chapter 2 Basic Statistics
    1. 2.1 Introduction
    2. 2.2 Sign Test
    3. 2.3 Signed-Rank Wilcoxon
      1. 2.3.1 Estimation and Confidence Intervals
      2. 2.3.2 Computation in R
    4. 2.4 Bootstrap
      1. 2.4.1 Percentile Bootstrap Confidence Intervals
      2. 2.4.2 Bootstrap Tests of Hypotheses
    5. 2.5 Robustness*
    6. 2.6 One- and Two-Sample Proportion Problems
      1. 2.6.1 One-Sample Problems
      2. 2.6.2 Two-Sample Problems
    7. 2.7 χ2 Tests
      1. 2.7.1 Goodness-of-Fit Tests for a Single Discrete Random Variable
        1. Confidence Intervals
      2. 2.7.2 Several Discrete Random Variables
        1. Confidence Intervals
      3. 2.7.3 Independence of Two Discrete Random Variables
        1. Confidence Intervals
      4. 2.7.4 McNemar’s Test
    8. 2.8 Exercises
      1. Figure 2.1
      2. Figure 2.2
      1. Table 2.1
  5. Chapter 3 Two-Sample Problems
    1. 3.1 Introductory Example
    2. 3.2 Rank-Based Analyses
      1. 3.2.1 Wilcoxon Test for Stochastic Ordering of Alternatives
      2. 3.2.2 Analyses for a Shift in Location
        1. Normal Scores
      3. 3.2.3 Analyses Based on General Score Functions
      4. 3.2.4 Linear Regression Model
    3. 3.3 Scale Problem
    4. 3.4 Placement Test for the Behrens–Fisher Problem
      1. Discussion
    5. 3.5 Efficiency and Optimal Scores*
      1. 3.5.1 Efficiency
    6. 3.6 Adaptive Rank Scores Tests
    7. 3.7 Exercises
      1. Figure 3.1
      2. Figure 3.2
      3. Figure 3.3
      4. Figure 3.4
      5. Figure 3.5
      6. Figure 3.6
      7. Figure 3.7
      8. Figure 3.8
      1. Table 3.1
      2. Table 3.2
  6. Chapter 4 Regression I
    1. 4.1 Introduction
    2. 4.2 Simple Linear Regression
    3. 4.3 Multiple Linear Regression
      1. 4.3.1 Multiple Regression
      2. 4.3.2 Polynomial Regression
    4. 4.4 Linear Models*
      1. 4.4.1 Estimation
      2. 4.4.2 Diagnostics
      3. 4.4.3 Inference
      4. 4.4.4 Confidence Interval for a Mean Response
    5. 4.5 Aligned Rank Tests*
    6. 4.6 Bootstrap
    7. 4.7 Nonparametric Regression
      1. 4.7.1 Polynomial Models
      2. 4.7.2 Nonparametric Regression
    8. 4.8 Correlation
      1. 4.8.1 Pearson’s Correlation Coefficient
      2. 4.8.2 Kendall’s τK
      3. 4.8.3 Spearman’s ρs
      4. 4.8.4 Computation and Examples
    9. 4.9 Exercises
      1. Figure 4.1
      2. Figure 4.2
      3. Figure 4.3
      4. Figure 4.4
      5. Figure 4.5
      6. Figure 4.6
      7. Figure 4.7
      8. Figure 4.8
      9. Figure 4.9
      10. Figure 4.10
      11. Figure 4.11
      12. Figure 4.12
      13. Figure 4.13
      1. Table 4.1
  7. Chapter 5 ANOVA and ANCOVA
    1. 5.1 Introduction
    2. 5.2 One-Way ANOVA
      1. 5.2.1 Multiple Comparisons
      2. 5.2.2 Kruskal–Wallis Test
    3. 5.3 Multi-Way Crossed Factorial Design
      1. 5.3.1 Two-Way
      2. 5.3.2 k-Way
    4. 5.4 ANCOVA*
      1. 5.4.1 Computation of Rank-Based ANCOVA
        1. Computation of Rank-Based ANCOVA for a One-Way Layout
        2. Computation of Rank-Based ANCOVA for a k-Way Layout
    5. 5.5 Methodology for Type III Hypotheses Testing*
    6. 5.6 Ordered Alternatives
    7. 5.7 Multi-Sample Scale Problem
    8. 5.8 Exercises
      1. Figure 5.1
      2. Figure 5.2
      3. Figure 5.3
      4. Figure 5.4
      5. Figure 5.5
      6. Figure 5.6
      7. Figure 5.7
  8. Chapter 6 Time to Event Analysis
    1. 6.1 Introduction
    2. 6.2 Kaplan–Meier and Log Rank Test
      1. 6.2.1 Gehan’s Test
    3. 6.3 Cox Proportional Hazards Models
    4. 6.4 Accelerated Failure Time Models
    5. 6.5 Exercises
      1. Figure 6.1
      2. Figure 6.2
      3. Figure 6.3
      4. Figure 6.4
      5. Figure 6.5
      6. Figure 6.6
      1. Table 6.1
      2. Table 6.2
      3. Table 6.3
      4. Table 6.4
  9. Chapter 7 Regression II
    1. 7.1 Introduction
    2. 7.2 High Breakdown Rank-Based Fits
      1. Stars Data
        1. 7.2.1 Weights for the HBR Fit
    3. 7.3 Robust Diagnostics
      1. 7.3.1 Graphics
      2. 7.3.2 Procedures for Differentiating between Robust Fits
      3. 7.3.3 Concluding Remarks
    4. 7.4 Weighted Regression
    5. 7.5 Linear Models with Skew Normal Errors
      1. 7.5.1 Sensitivity Analysis
      2. 7.5.2 Simulation Study
    6. 7.6 A Hogg-Type Adaptive Procedure
    7. 7.7 Nonlinear
      1. 7.7.1 Implementation of the Wilcoxon Nonlinear Fit
      2. 7.7.2 R Computation of Rank-Based Nonlinear Fits
      3. 7.7.3 Examples
        1. The 4 Parameter Logistic Model
      4. 7.7.4 High Breakdown Rank-Based Fits
    8. 7.8 Time Series
      1. 7.8.1 Order of the Autoregressive Series
    9. 7.9 Exercises
      1. Figure 7.1
      2. Figure 7.2
      3. Figure 7.3
      4. Figure 7.4
      5. Figure 7.5
      6. Figure 7.6
      7. Figure 7.7
      8. Figure 7.8
      9. Figure 7.9
      10. Figure 7.10
      11. Figure 7.11
      12. Figure 7.12
      13. Figure 7.13
      14. Figure 7.14
      15. Figure 7.15
      16. Figure 7.16
      17. Figure 7.17
      1. Table 7.1
      2. Table 7.2
      3. Table 7.3
      4. Table 7.4
  10. Chapter 8 Cluster Correlated Data
    1. 8.1 Introduction
    2. 8.2 Friedman’s Test
    3. 8.3 Joint Rankings Estimator
      1. 8.3.1 Estimates of Standard Error
        1. Compound Symmetric
        2. Empirical
        3. Sandwich Estimator
      2. 8.3.2 Inference
      3. 8.3.3 Examples
        1. Simulated Dataset
        2. Crabgrass Data
        3. Electric Resistance Data
    4. 8.4 Robust Variance Component Estimators
    5. 8.5 Multiple Rankings Estimator
      1. Estimation of Scale
      2. Inference
    6. 8.6 GEE-Type Estimator
      1. 8.6.1 Weights
      2. 8.6.2 Link Function
      3. 8.6.3 Working Covariance Matrix
      4. 8.6.4 Standard Errors
      5. 8.6.5 Examples
    7. 8.7 Exercises
      1. Figure 8.1
      2. Figure 8.2
      3. Figure 8.3
      1. Table 8.1
  11. Bibliography

Product information

  • Title: Nonparametric Statistical Methods Using R
  • Author(s): John Kloke, Joseph McKean
  • Release date: October 2014
  • Publisher(s): Chapman and Hall/CRC
  • ISBN: 9781498787277