Translations of Mathematical Monographs
2001; 216 pp; Hardcover
MSC: Primary 62; Secondary 60
Print ISBN: 978-0-8218-1183-2
Product Code: MMONO/196
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Asymptotic Statistical Methods for Stochastic ProcessesShare this page
Yu. N. Lin′kov
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 \(\epsilon\), Kakutani-Hellinger 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 information-theoretic problems of estimation of parameters are considered.
This English edition includes an extensive list of references and revised bibliographical notes.
Table of Contents
Table of Contents
Asymptotic Statistical Methods for Stochastic Processes
Graduate students and research mathematicians interested in statistics; engineers.