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.
1. Main Goals The theory of asset pricing has grown markedly more sophisticated in the last two decades, with the application of powerful mathematical tools such as probability theory, stochastic processes and numerical analysis. The main goal of this book is to provide a systematic exposition, with practical appli cations, of the no-arbitrage theory for asset pricing in financial engineering in the framework of a discrete time approach. The book should also serve well as a textbook on financial asset pricing. It should be accessible to a broad audi ence, in particular to practitioners in financial and related industries, as well as to students in MBA or graduate/advanced undergraduate programs in finance, financial engineering, financial econometrics, or financial information science. The no-arbitrage asset pricing theory is based on the simple and well ac cepted principle that financial asset prices are instantly adjusted at each mo ment in time in order not to allow an arbitrage opportunity. Here an arbitrage opportunity is an opportunity to have a portfolio of value aat an initial time lead to a positive terminal value with probability 1 (equivalently, at no risk), with money neither added nor subtracted from the portfolio in rebalancing dur ing the investment period. It is necessary for a portfolio of valueato include a short-sell position as well as a long-buy position of some assets.
Generalised Least Squares adopts a concise and mathematically rigorous approach. It will provide an up-to-date self-contained introduction to the unified theory of generalized least squares estimations, adopting a concise and mathematically rigorous approach. The book covers in depth the 'lower and upper bounds approach', pioneered by the first author, which is widely regarded as a very powerful and useful tool for generalized least squares estimation, helping the reader develop their understanding of the theory. The book also contains exercises at the end of each chapter and applications to statistics, econometrics, and biometrics, enabling use for self-study or as a course text.
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