Introduction to Robust Estimation and Hypothesis Testing,
Edition 4
By Rand R. Wilcox
Publication Date:
19 Sep 2016
Description
Introduction to Robust Estimating and Hypothesis Testing, 4th Editon, is a ‘how-to’ on the application of robust methods using available software. Modern robust methods provide improved techniques for dealing with outliers, skewed distribution curvature and heteroscedasticity that can provide substantial gains in power as well as a deeper, more accurate and more nuanced understanding of data. Since the last edition, there have been numerous advances and improvements. They include new techniques for comparing groups and measuring effect size as well as new methods for comparing quantiles. Many new regression methods have been added that include both parametric and nonparametric techniques. The methods related to ANCOVA have been expanded considerably. New perspectives related to discrete distributions with a relatively small sample space are described as well as new results relevant to the shift function. The practical importance of these methods is illustrated using data from real world studies. The R package written for this book now contains over 1200 functions.
New to this edition
- 35% revised content
- Covers many new and improved R functions
- New techniques that deal with a wide range of situations
Key Features
- Extensive revisions to cover the latest developments in robust regression
- Covers latest improvements in ANOVA
- Includes newest rank-based methods
- Describes and illustrated easy to use software
About the author
By Rand R. Wilcox, University of Southern California, USA
Table of Contents
- Preface
- Chapter 1: Introduction
- Abstract
- 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
- Abstract
- 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
- Abstract
- 3.1. A Bootstrap Estimate of a Standard Error
- 3.2. Density Estimators
- 3.3. The Sample 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: Confidence Intervals in the One-Sample Case
- Abstract
- 4.1. Problems when Working with Means
- 4.2. The g-and-h Distribution
- 4.3. Inferences About the Trimmed and 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. Concluding Remarks
- 4.9. Exercises
- References
- Chapter 5: Comparing Two Groups
- Abstract
- 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. Rank-Based Methods and a Probabilistic Measure of Effect Size
- 5.8. Comparing Two Independent Binomial and Multinomial Distributions
- 5.9. Comparing Dependent Groups
- 5.10. Exercises
- References
- Chapter 6: Some Multivariate Methods
- Abstract
- 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. Comparing OP Measures of Location
- 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 Components Analysis
- 6.15. Cluster Analysis
- 6.16. Multivariate Discriminate Analysis
- 6.17. Exercises
- References
- Chapter 7: One-Way and Higher Designs for Independent Groups
- Abstract
- 7.1. Trimmed Means and a One-Way Design
- 7.2. Two-Way Designs and Trimmed Means
- 7.3. Three-Way Designs and Trimmed Means Including Medians
- 7.4. Multiple Comparisons Based on Medians and Other Trimmed Means
- 7.5. A Random Effects Model for Trimmed Means
- 7.6. Global Tests Based on M-Measures of Location
- 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. Exercises
- References
- Chapter 8: Comparing Multiple Dependent Groups
- Abstract
- 8.1. Comparing Trimmed Means
- 8.2. Bootstrap Methods Based on Marginal Distributions
- 8.3. Bootstrap Methods Based on Difference Scores
- 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. Some Rank-Based Multivariate Methods
- 8.8. Three-Way Designs
- 8.9. Exercises
- References
- Chapter 9: Correlation and Tests of Independence
- Abstract
- 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
- Abstract
- 10.1. Problems with Ordinary Least Squares
- 10.2. 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
- Abstract
- 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 Nonparametric Regression
- 11.6. Checking the Specification of a Regression Model
- 11.7. Regression Interactions and Moderator Analysis
- 11.8. Comparing Parametric, Additive and Nonparametric 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
- Abstract
- 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 Covariates when There Is Curvature
- 12.4. Some Global Tests
- 12.5. Methods for Dependent Groups
- 12.6. Exercises
- References
- References
- Index
Book details
ISBN:
9780128047330
Page Count: 810
Retail Price
:
£93.99
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Audience
The book is relevant to anyone dealing with methods for studying associations, comparing groups, or analyzing multivariate data. The book assumes the reader has had some basic training in statistics
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