Introduction to Robust Estimation and Hypothesis Testing

Preface

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 Using the Computer: R

1.9 Some Data Management Issues

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

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 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

Chapter 4. Confidence Intervals 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 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

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 Inferences About a Probabilistic Measure of Effect Size

5.8 Comparing Two Independent Binomials

5.9 Comparing Dependent Groups

5.10 Exercises

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 Inference in the One-Sample Case

6.8 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 Components Analysis

6.15 Cluster Analysis

6.16 Exercises

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 and Trimmed Means

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

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

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

Chapter 9. Correlation and Tests of Independence

9.1 Problems with the Product Moment 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

Chapter 10. Robust Regression

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

Chapter 11. More Regression Methods

11.1 Inferences About Robust Regression Parameters

11.2 Comparing the Parameters of Two Independent 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 ANCOVA

11.12 Marginal Longitudinal Data Analysis: Comments on Comparing Groups

11.13 Exercises

Index