Robustness of Statistical Tests

Takeaki Kariya, Bimal K. Sinha, Gerald L. Lieberman, Ingram Olkin

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9780123982308
• eBook ISBN: 9781483266008
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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.

Table of contents

• Front Cover
• Robustness of Statistical Tests
• Copyright Page
• Table of Contents
• Dedication
• Preface
• Introduction
• Chapter 1. Spherically Symmetric Distributions
• Chapter 2. Invariance Approach to Testing
• Chapter 3. General Approach to the Robustness of Tests
• Chapter 4. Robustness of t-Test and Tests for Serial Correlation
• Chapter 5. General Multivariate Analysis of Variance(GMANOVA)
• Chapter 6. Tests for Covariance Structures
• Chapter 7. Detection of Outliers
• Chapter 8. Two-Population Problems
• References
• Author Index
• Subject Index