Introduction to Robust Estimation and Hypothesis Testing, 4/e (Hardcover)

<內容簡介>

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
<章節目錄>

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

內容簡介：

《強健估計與假設檢定入門，第四版》是一本介紹如何使用現有軟體應用強健方法的書籍。現代的強健方法提供了處理離群值、偏斜分佈曲率和異方差性的改進技術，這些技術可以在功效上帶來顯著的增益，並且對數據的理解更深入、更準確、更細緻。自上一版以來，已經有許多進展和改進。這些包括比較群組和測量效應大小的新技術，以及比較分位數的新方法。新增了許多包括參數和非參數技術的回歸方法。與ANCOVA相關的方法也大大擴展了。還描述了與相對較小樣本空間的離散分佈相關的新觀點，以及與位移函數相關的新結果。通過使用真實世界研究的數據來說明這些方法的實際重要性。為本書編寫的R軟體包現在包含超過1200個函數。

本版新增內容：
- 修訂內容佔35%
- 包含許多新的和改進的R函數
- 新的技術可以應對各種情況

章節目錄：

前言
第1章：引言
摘要
1.1. 假設正態性的問題
1.2. 轉換
1.3. 影響曲線
1.4. 中心極限定理
1.5. ANOVA F是否強健？
1.6. 迴歸
1.7. 更多備註
1.8. R軟體
1.9. 一些數據管理問題
1.10. 數據集
參考文獻
第2章：強健方法的基礎
摘要
2.1. 判斷強健性的基本工具
2.2. 一些位置測量及其影響函數
2.3. 尺度測量
2.4. 尺度等變M-位置測量
2.5. Winsorized 期望值
參考文獻
第3章：位置和尺度測量的估計
摘要
3.1. 標準誤的自助法估計
3.2. 密度估計
3.3. 樣本修剪平均數
3.4. 有限樣本斷裂點
3.5. 估計分位數
3.6. 位置的M-估計
3.7. 一步M-估計
3.8. W-估計
3.9. Hodges-Lehmann 估計
3.10. 跳過估計
3.11. 位置估計的比較
3.12. 更多尺度測量
3.13. 一些離群值檢測方法
3.14. 練習
參考文獻
第4章：單樣本情況下的置信區間
摘要
4.1. 處理平均數時的問題
4.2. g和h分佈
4.3. 關於修剪和Winsorized平均數的推論
4.4. 基本自助法方法
4.5. 關於M-估計的推論
4.6. 分位數的置信區間
4.7. 經驗概似度
4.8. 結論
4.9. 練習
參考文獻