Robustness of Statistical Tests

PrefaceIntroductionChapter 1 Spherically Symmetric Distributions 1.1 Why Normal and Why Not Spherical? 1.2 Elliptically Symmetric Distributions 1.3 Left-Orthogonally Invariant Distributions ExercisesChapter 2 Invariance Approach to Testing 2.1 Invariant Measures on Groups 2.2 Invariant Measures on Homogeneous Spaces 2.3 A Review of the Theory of Testing of Hypotheses 2.4 Distribution of a Maximal Invariant Appendix to Chapter 2, Section 4 ExercisesChapter 3 General Approach to the Robustness of Tests 3.1 Null, Nonnull and Optimality Robustness 3.2 Outline of Testing Problems Under Normality 3.3 General Theory on Null Robustness 3.4 General Theory on Nonnull Robustness 3.5 General Approach to Optimality Robustness ExercisesChapter 4 Robustness of t-Test and Tests for Serial Correlation 4.1 Formulation of the Problem 4.2 One-Sided Testing Problems Without Invariance 4.3 Two-Sided Testing Problems Without Invariance 4.4 UMPI Property of t-Test 4.5 Tests on Serial Correlation Without Invariance ExercisesChapter 5 General Multivariate Analysis of Variance (GMANOVA) 5.1 Introduction 5.2 GMANOVA Model and Problem 5.3 MANOVA Problem 5.4 GMANOVA Problem Appendix ExercisesChapter 6 Tests for Covariance Structures 6.1 Introduction 6.2 Testing ∑12 = 0 6.3 Testing Sphericity 6.4 Testing ∑ = I vs ∑ > I ExercisesChapter 7 Detection of Outliers 7.1 Introduction 7.2 Test for Mean Slippage 7.3 Test for Dispersion Slippage Appendix ExercisesChapter 8 Two-Population Problems 8.1 Introduction 8.2 Test of Equality of Two Location Parameters—Nonnormal Case 8.3 Test of Equality of Two Location Parameters—Nonexponential Case 8.4 Test of Equality of Two Scale Parameters—Nonnormal Case 8.5 Test of Equality of Two Scale Parameters—Nonexponential Case ExercisesReferencesAuthor IndexSubject Index