Introduction to Robust Estimation and Hypothesis Testing

5th Edition - September 18, 2021
Author: Rand R. Wilcox
Language: English
Paperback ISBN:
9 7 8 - 0 - 1 2 - 8 2 0 0 9 8 - 8
eBook ISBN:
9 7 8 - 0 - 1 2 - 8 2 0 0 9 9 - 5

Introduction to Robust Estimating and Hypothesis Testing, Fifth Edition is a useful ‘how-to’ on the application of robust methods utilizing easy-to-use software. This truste… Read more

Introduction to Robust Estimation and Hypothesis Testing

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Introduction to Robust Estimating and Hypothesis Testing, Fifth Edition is a useful ‘how-to’ on the application of robust methods utilizing easy-to-use software. This trusted resource provides an overview of modern robust methods, including improved techniques for dealing with outliers, skewed distribution curvature, and heteroscedasticity that can provide substantial gains in power. Coverage includes techniques for comparing groups and measuring effect size, current methods for comparing quantiles, and expanded regression methods for both parametric and nonparametric techniques. The practical importance of these varied methods is illustrated using data from real world studies. Over 1700 R functions are included to support comprehension and practice.

Cover image
Title page
Table of Contents
Copyright
Dedication
Preface
References
Chapter 1: Introduction
1.1. Problems With Assuming Normality
1.2. Transformations
1.3. The Influence Curve
1.4. The Central Limit Theorem
1.5. Is the ANOVA F Robust?
1.6. Regression
1.7. More Remarks
1.8. R Software
1.9. Some Data Management Issues
1.10. Data Sets
References
Chapter 2: A Foundation for Robust Methods
2.1. Basic Tools for Judging Robustness
2.2. Some Measures of Location and Their Influence Function
2.3. Measures of Scale
2.4. Scale-Equivariant M-Measures of Location
2.5. Winsorized Expected Values
References
Chapter 3: Estimating Measures of Location and Scale
3.1. A Bootstrap Estimate of a Standard Error
3.2. Density Estimators
3.3. The Sample Median and Trimmed Mean
3.4. The Finite Sample Breakdown Point
3.5. Estimating Quantiles
3.6. An M-Estimator of Location
3.7. One-Step M-Estimator
3.8. W-Estimators
3.9. The Hodges–Lehmann Estimator
3.10. Skipped Estimators
3.11. Some Comparisons of the Location Estimators
3.12. More Measures of Scale
3.13. Some Outlier Detection Methods
3.14. Exercises
References
Chapter 4: Inferences in the One-Sample Case
4.1. Problems When Working With Means
4.2. The g-and-h Distribution
4.3. Inferences About the Trimmed, Winsorized Means
4.4. Basic Bootstrap Methods
4.5. Inferences About M-Estimators
4.6. Confidence Intervals for Quantiles
4.7. Empirical Likelihood
4.8. Inferences About the Probability of Success
4.9. Concluding Remarks
4.10. Exercises
References
Chapter 5: Comparing Two Groups
5.1. The Shift Function
5.2. Student's T Test
5.3. Comparing Medians and Other Trimmed Means
5.4. Inferences Based on a Percentile Bootstrap Method
5.5. Comparing Measures of Scale
5.6. Permutation Tests
5.7. Methods Based on Ranks and the Typical Difference
5.8. Comparing Two Independent Binomial and Multinomial Distributions
5.9. Comparing Dependent Groups
5.10. Exercises
References
Chapter 6: Some Multivariate Methods
6.1. Generalized Variance
6.2. Depth
6.3. Some Affine Equivariant Estimators
6.4. Multivariate Outlier Detection Methods
6.5. A Skipped Estimator of Location and Scatter
6.6. Robust Generalized Variance
6.7. Multivariate Location: Inference in the One-Sample Case
6.8. The Two-Sample Case
6.9. Multivariate Density Estimators
6.10. A Two-Sample, Projection-Type Extension of the Wilcoxon–Mann–Whitney Test
6.11. A Relative Depth Analog of the Wilcoxon–Mann–Whitney Test
6.12. Comparisons Based on Depth
6.13. Comparing Dependent Groups Based on All Pairwise Differences
6.14. Robust Principal Component Analysis
6.15. Cluster Analysis
6.16. Classification Methods
6.17. Exercises
References
Chapter 7: One-Way and Higher Designs for Independent Groups
7.1. Trimmed Means and a One-Way Design
7.2. Two-Way Designs and Trimmed Means
7.3. Three-Way Designs, Trimmed Means, and Medians
7.4. Multiple Comparisons Based on Medians and Other Trimmed Means
7.5. A Random Effects Model for Trimmed Means
7.6. Bootstrap Global Tests
7.7. M-Measures of Location and a Two-Way Design
7.8. Ranked-Based Methods for a One-Way Design
7.9. A Rank-Based Method for a Two-Way Design
7.10. MANOVA Based on Trimmed Means
7.11. Nested Designs
7.12. Methods for Binary Data
7.13. Exercises
References
Chapter 8: Comparing Multiple Dependent Groups
8.1. Comparing Trimmed Means
8.2. Bootstrap Methods Based on Marginal Distributions
8.3. Bootstrap Methods Based on Difference Scores and a Measure of Effect Size
8.4. Comments on Which Method to Use
8.5. Some Rank-Based Methods
8.6. Between-by-Within and Within-by-Within Designs
8.7. Three-Way Designs
8.8. Exercises
References
Chapter 9: Correlation and Tests of Independence
9.1. Problems With Pearson's Correlation
9.2. Two Types of Robust Correlations
9.3. Some Type M Measures of Correlation
9.4. Some Type O Correlations
9.5. A Test of Independence Sensitive to Curvature
9.6. Comparing Correlations: Independent Case
9.7. Exercises
References
Chapter 10: Robust Regression
10.1. Problems With Ordinary Least Squares
10.2. The Theil–Sen Estimator
10.3. Least Median of Squares
10.4. Least Trimmed Squares Estimator
10.5. Least Trimmed Absolute Value Estimator
10.6. M-Estimators
10.7. The Hat Matrix
10.8. Generalized M-Estimators
10.9. The Coakley–Hettmansperger and Yohai Estimators
10.10. Skipped Estimators
10.11. Deepest Regression Line
10.12. A Criticism of Methods With a High Breakdown Point
10.13. Some Additional Estimators
10.14. Comments About Various Estimators
10.15. Outlier Detection Based on a Robust Fit
10.16. Logistic Regression and the General Linear Model
10.17. Multivariate Regression
10.18. Exercises
References
Chapter 11: More Regression Methods
11.1. Inferences About Robust Regression Parameters
11.2. Comparing the Regression Parameters of J≥2 Groups
11.3. Detecting Heteroscedasticity
11.4. Curvature and Half-Slope Ratios
11.5. Curvature and Non-Parametric Regression
11.6. Checking the Specification of a Regression Model
11.7. Regression Interactions and Moderator Analysis
11.8. Comparing Parametric, Additive, and Non-Parametric Fits
11.9. Measuring the Strength of an Association Given a Fit to the Data
11.10. Comparing Predictors
11.11. Marginal Longitudinal Data Analysis: Comments on Comparing Groups
11.12. Exercises
References
Chapter 12: ANCOVA
12.1. Methods Based on Specific Design Points and a Linear Model
12.2. Methods When There Is Curvature and a Single Covariate
12.3. Dealing With Two or More Covariates When There Is Curvature
12.4. Some Global Tests
12.5. Methods for Dependent Groups
12.6. Exercises
References
References
References
Index

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