Kariya / Sinha / Lieberman Robustness of Statistical Tests

1. Auflage 2014
ISBN: 978-1-4832-6600-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 208 Seiten, Web PDF

Robustness of Statistical Tests provides a general, systematic finite sample theory of the robustness of tests and covers the application of this theory to some important testing problems commonly considered under normality. This eight-chapter text focuses on the robustness that is concerned with the exact robustness in which the distributional or optimal property that a test carries under a normal distribution holds exactly under a nonnormal distribution. Chapter 1 reviews the elliptically symmetric distributions and their properties, while Chapter 2 describes the representation theorem for the probability ration of a maximal invariant. Chapter 3 explores the basic concepts of three aspects of the robustness of tests, namely, null, nonnull, and optimality, as well as a theory providing methods to establish them. Chapter 4 discusses the applications of the general theory with the study of the robustness of the familiar Student's r-test and tests for serial correlation. This chapter also deals with robustness without invariance. Chapter 5 looks into the most useful and widely applied problems in multivariate testing, including the GMANOVA (General Multivariate Analysis of Variance). Chapters 6 and 7 tackle the robust tests for covariance structures, such as sphericity and independence and provide a detailed description of univariate and multivariate outlier problems. Chapter 8 presents some new robustness results, which deal with inference in two population problems. This book will prove useful to advance graduate mathematical statistics students.

Autoren/Hrsg.

Kariya, Takeaki

Sinha, Bimal K.

Lieberman, Gerald L.

Olkin, Ingram

Inhaltsverzeichnis

1;Front Cover;1
2;Robustness of Statistical Tests;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface;10
7;Introduction;14
8;Chapter 1. Spherically Symmetric Distributions;18
8.1;1.1. Why Normal and Why Not Spherical?;18
8.2;1.2. Elliptically Symmetric Distributions;21
8.3;1.3. Left-Orthogonally Invariant Distributions;26
8.4;Exercises;30
9;Chapter 2. Invariance Approach to Testing;32
9.1;2.1. Invariant Measures on Groups;32
9.2;2.2. Invariant Measures on Homogeneous Spaces;38
9.3;2.3. A Review of the Theory of Testing of Hypotheses;41
9.4;2.4. Distribution of a Maximal Invariant;47
9.5;Appendix to Chapter 2, Section 4;51
9.6;Exercises;54
10;Chapter 3. General Approach to the Robustness of Tests;56
10.1;3.1. Null, Nonnull, and Optimally Robustness;56
10.2;3.2. Outline of Testing Problems under Normality;59
10.3;3.3. General Theory on Null Robustness;66
10.4;3.4. General Theory on Nonnull Robustness;79
10.5;3.5. General Approach to Optimality Robustness;91
10.6;Exercises;96
11;Chapter 4. Robustness of t-Test and Tests for Serial Correlation;98
11.1;4.1. Formulation of the Problem;98
11.2;4.2. One-Sided Testing Problems without Invariance;102
11.3;4.3. Two-Sided Testing Problems without Invariance;106
11.4;4.4. UMPI Property of t-Test;110
11.5;4.5. Tests on Serial Correlation without Invariance;112
11.6;Exercises;118
12;Chapter 5. General Multivariate Analysis of Variance(GMANOVA);120
12.1;5.1. Introduction;120
12.2;5.2. GMANOVA Model and Problem;121
12.3;5.3. MANOVA Problem;131
12.4;5.4. GMANOVA Problem;135
12.5;Appendix;146
12.6;Exercises;148
13;Chapter 6. Tests for Covariance Structures;150
13.1;6.1. Introduction;150
13.2;6.2. Testing S12 = 0;151
13.3;6.3. Testing Sphericity;157
13.4;6.3. Testing Sphericity;157
13.5;Exercises;161
14;Chapter 7. Detection of Outliers;162
14.1;7.1. Introduction;162
14.2;7.2. Test for Mean Slippage;163
14.3;7.3. Test for Dispersion Slippage;175
14.4;Appendix;181
14.5;Exercises;183
15;Chapter 8. Two-Population Problems;184
15.1;8.1. Introduction;184
15.2;8.2. Test of Equality of Two Location Parameters -Nonnormal Case;185
15.3;8.3. Test of Equality of Two Location Parameters-Nonexponential Case;188
15.4;8.4. Test of Equality of Two Scale Parameters—Nonnormal Case;190
15.5;8.5. Test of Equality of Two Scale Parameters–Nonexponential Case;192
15.6;Exercises;194
16;References;196
17;Author Index;202
18;Subject Index;204