Robustness of Statistical Tests 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.