Translations of Mathematical Monographs 2001; 216 pp; hardcover Volume: 196 ISBN10: 0821811835 ISBN13: 9780821811832 List Price: US$97 Member Price: US$77.60 Order Code: MMONO/196
 The asymptotic properties of the likelihood ratio play an important part in solving problems in statistics for various schemes of observations. In this book, the author describes the asymptotic methods for parameter estimation and hypothesis testing based on asymptotic properties of the likelihood ratios in the case where an observed stochastic process is a semimartingale. Chapter 1 gives the general basic notions and results of the theory under consideration. Chapters 2 and 3 are devoted to the problem of distinguishing between two simple statistical hypotheses. In Chapter 2, certain types of asymptotic distinguishability between families of hypotheses are introduced. The types are characterized in terms of likelihood ratio, Hellinger integral of order \(\epsilon\), KakutaniHellinger distance, and the distance in variation between hypothetical measures, etc. The results in Chapter 2 are used in Chapter 3 in statistical experiments generated by observations of semimartingales. Chapter 4 applies the general limit theorems on asymptotic properties of maximum likelihood and Bayes estimates obtained by Ibragimov and Has'minskii for observations of an arbitrary nature to observations of semimartingales. In Chapter 5, an unknown parameter is assumed to be random, and under this condition, certain informationtheoretic problems of estimation of parameters are considered. This English edition includes an extensive list of references and revised bibliographical notes. Readership Graduate students and research mathematicians interested in statistics; engineers. Table of Contents  Local densities of measures and limit theorems for stochastic processes
 Asymptotic distinguishing between simple hypotheses in the scheme of general statistical experiments
 Asymptotic behavior of the likelihood ratio in problems of distinguishing between simple hypotheses for semimartingales
 Asymptotic estimation of parameters
 Asymptotic informationtheoretic problems in parameter estimation
 Bibliographical notes
 References
 Index
