Elsevier S & T

Introduction to Robust Estimation and Hypothesis Testing

Wilcox, Rand R.

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Table of contents
  • Cover
  • Contentsiii
  • Prefacexvii
  • Chapter 1. Introduction1
  • 1.1 Problems with Assuming Normality2
  • 1.2 Transformations6
  • 1.3 The Influence Curve7
  • 1.4 The Central Limit Theorem8
  • 1.5 Is the ANOVA F Robust?9
  • 1.6 Regression10
  • 1.7 More Remarks10
  • 1.8 Using the Computer: R and S-PLUS11
  • 1.9 Some Data-Managment Issues13
  • Chapter 2. A Foundation for Robust Methods19
  • 2.1 Basic Tools for Judging Robustness20
  • 2.2 Some Measures of Location and Their Influence Function26
  • 2.3 Measures of Scale33
  • 2.4 Scale-Equivariant M-Measures of Location36
  • 2.5 Winsorized Expected Values38
  • Chapter 3. Estimating Measures of Location and Scale43
  • 3.1 A Bootstrap Estimate of a Standard Error44
  • 3.2 Density Estimators47
  • 3.3 The Sample Trimmed Mean56
  • 3.4 The Finite-Sample Breakdown Point65
  • 3.5 Estimating Quantiles66
  • 3.6 An M-Estimator of Location73
  • 3.7 One-Step M-Estimator85
  • 3.8 W-Estimators87
  • 3.9 The Hodges–Lehmann Estimator88
  • 3.10 Skipped Estimators88
  • 3.11 Some Comparisons of the Location Estimators90
  • 3.12 More Measures of Scale92
  • 3.13 Some Outlier Detection Methods99
  • 3.14 Exercises102
  • Chapter 4. Confidence Intervals in the One-Sample Case105
  • 4.1 Problems When Working with Means105
  • 4.2 The g-and-h Distribution110
  • 4.3 Inferences About the Trimmed Mean113
  • 4.4 Basic Bootstrap Methods117
  • 4.5 Inferences About M-Estimators127
  • 4.6 Confidence Intervals for Quantiles130
  • 4.7 Concluding Remarks134
  • 4.8 Exercises135
  • Chapter 5. Comparing Two Groups137
  • 5.1 The Shift Function139
  • 5.2 Student’s t Test155
  • 5.3 The Yuen–Welch Test159
  • 5.4 Inferences Based on a Percentile Bootstrap Method167
  • 5.5 Comparing Measures of Scale170
  • 5.6 Permutation Tests172
  • 5.7 Some Heteroscedastic, Rank-Based Methods173
  • 5.8 Comparing Two Independent Binomials181
  • 5.9 Comparing Dependent Groups184
  • 5.10 Exercises199
  • Chapter 6. Some Multivariate Methods203
  • 6.1 Generalized Variance203
  • 6.2 Depth204
  • 6.3 Some Affine-Equivariant Estimators214
  • 6.4 Multivariate Outlier Detection Methods221
  • 6.5 A Skipped Estimator of Location and Scatter236
  • 6.6 Confidence Region and Inference Based on the OP Estimator of Location240
  • 6.7 Two-Sample Case244
  • 6.8 Multivariate Density Estimators245
  • 6.9 A Two-Sample, Projection–Type Extension of the Wilcoxon–Mann–Whitney Test247
  • 6.10 A Relative Depth Analog of the Wilcoxon–Mann–Whitney Test250
  • 6.11 Comparisons Based on Depth253
  • 6.12 Comparing Dependent Groups Based on All Pairwise Differences259
  • 6.13 Exercises262
  • Chapter 7. One-Way and Higher Designs for Independent Groups265
  • 7.1 Trimmed Means and a One-Way Design266
  • 7.2 Two-Way Designs and Trimmed Means275
  • 7.3 Three-Way Designs and Trimmed Means284
  • 7.4 Multiple Comparisons Based on Trimmed Means289
  • 7.5 A Random Effects Model for Trimmed Means302
  • 7.6 Bootstrap Methods and M-Measures of Location307
  • 7.7 M-Measures of Location and a Two-Way Design316
  • 7.8 Ranked-Based Methods for a One-Way Design319
  • 7.9 A Rank-Based Method for a Two-Way Design324
  • 7.10 Exercises328
  • Chapter 8. Comparing Multiple Dependent Groups333
  • 8.1 Comparing Trimmed Means333
  • 8.2 Bootstrap Methods Based on Marginal Distributions342
  • 8.3 Percentile Bootstrap Methods Based on Difference Scores353
  • 8.4 Comments on Which Method to Use358
  • 8.5 Some Rank-Based Methods359
  • 8.6 A Split-Plot Design360
  • 8.7 Some Rank-Based Multivariate Methods377
  • 8.8 Exercises382
  • Chapter 9. Correlation and Tests of Independence383
  • 9.1 Problems with the Product Moment Correlation384
  • 9.2 Two Types of Robust Correlations389
  • 9.3 Some Type M Measures of Correlation389
  • 9.4 Some Type O Correlations404
  • 9.5 A Test of Independence Sensitive to Curvature or a Linear Association408
  • 9.6 Exercises411
  • Chapter 10. Robust Regression413
  • 10.1 Problems with Ordinary Least Squares415
  • 10.2 Theil–Sen Estimator423
  • 10.3 Least Median of Squares427
  • 10.4 Least Trimmed Squares Estimator428
  • 10.5 Least Trimmed Absolute Value Estimator428
  • 10.6 M-Estimators429
  • 10.7 The Hat Matrix431
  • 10.8 Generalized M-Estimators434
  • 10.9 The Coakley–Hettmansperger Estimator438
  • 10.10 Skipped Estimators440
  • 10.11 Deepest Regression Line442
  • 10.12 A Criticism of Methods with a High Breakdown Point443
  • 10.13 Some Additional Estimators443
  • 10.14 Comments About Various Estimators455
  • 10.15 Detecting Regression Outliers462
  • 10.16 Exercises464
  • Chapter 11. More Regression Methods467
  • 11.1 Inferential Methods Based on Robust Estimators467
  • 11.2 Comparing the Parameters of Two Independent Groups480
  • 11.3 Curvature and Half-Slope Ratios484
  • 11.4 Curvature and Nonparametric Regression488
  • 11.5 Checking the Specification of a Regression Model511
  • 11.6 Detecting Interactions517
  • 11.7 Comparing Parametric, Additive, and Nonparametric Fits520
  • 11.8 ANCOVA522
  • 11.9 Exercises534
  • References537
  • Index575
Book details
  • Vendor Elsevier S & T
  • SKU 9780127515427
  • ISBN-13 9780080470535
  • Author Wilcox, Rand R.
  • Edition 2nd
  • Category Mathematics
  • Subject Regression Analysis

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This revised book provides a thorough explanation of the foundation of robust methods, incorporating the latest updates on R and S-Plus, robust ANOVA (Analysis of Variance) and regression. It guides advanced students and other professionals through the basic strategies used for developing practical solutions to problems, and provides a brief background on the foundations of modern methods, placing the new methods in historical context. Author Rand Wilcox includes chapter exercises and many real-world examples that illustrate how various methods perform in different situations.

Introduction to Robust Estimation and Hypothesis Testing, Second Edition, focuses on the practical applications of modern, robust methods which can greatly enhance our chances of detecting true differences among groups and true associations among variables.

* Covers latest developments in robust regression
* Covers latest improvements in ANOVA
* Includes newest rank-based methods
* Describes and illustrated easy to use software