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Asymptotic Statistical Methods for Stochastic Processes

Yu. N. Lin′kov Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine
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Hardcover ISBN: 978-0-8218-1183-2
Product Code: MMONO/196
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AMS Member Price: $82.40 Electronic ISBN: 978-1-4704-4622-2 Product Code: MMONO/196.E List Price:$97.00
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List Price: $154.50 MAA Member Price:$139.05
AMS Member Price: $123.60 Click above image for expanded view Asymptotic Statistical Methods for Stochastic Processes Yu. N. Lin′kov Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine Available Formats:  Hardcover ISBN: 978-0-8218-1183-2 Product Code: MMONO/196  List Price:$103.00 MAA Member Price: $92.70 AMS Member Price:$82.40
 Electronic ISBN: 978-1-4704-4622-2 Product Code: MMONO/196.E
 List Price: $97.00 MAA Member Price:$87.30 AMS Member Price: $77.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$154.50 MAA Member Price: $139.05 AMS Member Price:$123.60
• Book Details

Translations of Mathematical Monographs
Volume: 1962001; 216 pp
MSC: Primary 62; Secondary 60;

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.

Graduate students and research mathematicians interested in statistics; engineers.

• Chapters
• 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
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Volume: 1962001; 216 pp
MSC: Primary 62; Secondary 60;

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.