Asymptotic statistical methods for stochastic processes


Asymptotic statistical methods for stochastic processes

Yu. N. Linʹkov ; [translated from the Russian by Victor Kotov]

(Translations of mathematical monographs, v. 196)

American Mathematical Society, c2001


Asimptoticheskie metody statistiki sluchaĭnykh prot︠s︡essov

Асимптотические методы статистики случайных процессов

大学図書館所蔵 件 / 45



Includes bibliographical references (p. 203-212) and index



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.


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 information-theoretic problems in parameter estimation Bibliographical notes References Index.

「Nielsen BookData」 より

関連文献: 1件中  1-1を表示