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Asymptotic Methods in Probability and Statistics with Applications

Author : N. Balakrishnan

Publisher : Springer Science & Business Media

Page : 584 pages

File Size : 31,2 MB

Release : 2001-06-21

Category : Business & Economics

ISBN : 9780817642143

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Book Description

Traditions of the 150-year-old St. Petersburg School of Probability and Statis tics had been developed by many prominent scientists including P. L. Cheby chev, A. M. Lyapunov, A. A. Markov, S. N. Bernstein, and Yu. V. Linnik. In 1948, the Chair of Probability and Statistics was established at the Department of Mathematics and Mechanics of the St. Petersburg State University with Yu. V. Linik being its founder and also the first Chair. Nowadays, alumni of this Chair are spread around Russia, Lithuania, France, Germany, Sweden, China, the United States, and Canada. The fiftieth anniversary of this Chair was celebrated by an International Conference, which was held in St. Petersburg from June 24-28, 1998. More than 125 probabilists and statisticians from 18 countries (Azerbaijan, Canada, Finland, France, Germany, Hungary, Israel, Italy, Lithuania, The Netherlands, Norway, Poland, Russia, Taiwan, Turkey, Ukraine, Uzbekistan, and the United States) participated in this International Conference in order to discuss the current state and perspectives of Probability and Mathematical Statistics. The conference was organized jointly by St. Petersburg State University, St. Petersburg branch of Mathematical Institute, and the Euler Institute, and was partially sponsored by the Russian Foundation of Basic Researches. The main theme of the Conference was chosen in the tradition of the St.



Asymptotic Theory of Statistics and Probability

Author : Anirban DasGupta

Publisher : Springer Science & Business Media

Page : 726 pages

File Size : 50,59 MB

Release : 2008-03-07

Category : Mathematics

ISBN : 0387759700

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Book Description

This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.



Asymptotic Statistics

Author : A. W. van der Vaart

Publisher : Cambridge University Press

Page : 470 pages

File Size : 34,46 MB

Release : 2000-06-19

Category : Mathematics

ISBN : 9780521784504

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Book Description

This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master s level statistics text, this book will also give researchers an overview of the latest research in asymptotic statistics.





From Finite Sample to Asymptotic Methods in Statistics

Author : Pranab K. Sen

Publisher : Cambridge University Press

Page : 399 pages

File Size : 47,18 MB

Release : 2010

Category : Mathematics

ISBN : 0521877229

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Book Description

A broad view of exact statistical inference and the development of asymptotic statistical inference.



Statistical Estimation

Author : I.A. Ibragimov

Publisher : Springer Science & Business Media

Page : 410 pages

File Size : 15,6 MB

Release : 2013-11-11

Category : Mathematics

ISBN : 1489900276

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Book Description

when certain parameters in the problem tend to limiting values (for example, when the sample size increases indefinitely, the intensity of the noise ap proaches zero, etc.) To address the problem of asymptotically optimal estimators consider the following important case. Let X 1, X 2, ... , X n be independent observations with the joint probability density !(x,O) (with respect to the Lebesgue measure on the real line) which depends on the unknown patameter o e 9 c R1. It is required to derive the best (asymptotically) estimator 0:( X b ... , X n) of the parameter O. The first question which arises in connection with this problem is how to compare different estimators or, equivalently, how to assess their quality, in terms of the mean square deviation from the parameter or perhaps in some other way. The presently accepted approach to this problem, resulting from A. Wald's contributions, is as follows: introduce a nonnegative function w(0l> ( ), Ob Oe 9 (the loss function) and given two estimators Of and O! n 2 2 the estimator for which the expected loss (risk) Eown(Oj, 0), j = 1 or 2, is smallest is called the better with respect to Wn at point 0 (here EoO is the expectation evaluated under the assumption that the true value of the parameter is 0). Obviously, such a method of comparison is not without its defects.



Asymptotic Analysis of Random Walks

Author : A. A. Borovkov

Publisher : Cambridge University Press

Page : 437 pages

File Size : 47,33 MB

Release : 2020-10-29

Category : Mathematics

ISBN : 1108901204

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Book Description

This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.



Expansions and Asymptotics for Statistics

Author : Christopher G. Small

Publisher : CRC Press

Page : 359 pages

File Size : 24,24 MB

Release : 2010-05-07

Category : Mathematics

ISBN : 1420011022

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Book Description

Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptoti



Stochastic Geometry, Spatial Statistics and Random Fields

Author : Evgeny Spodarev

Publisher : Springer

Page : 470 pages

File Size : 13,63 MB

Release : 2013-02-11

Category : Mathematics

ISBN : 3642333052

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Book Description

This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.



Analytical and Computational Methods in Probability Theory

Author : Vladimir V. Rykov

Publisher : Springer

Page : 551 pages

File Size : 31,14 MB

Release : 2017-12-21

Category : Computers

ISBN : 3319715046

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Book Description

This book constitutes the refereed proceedings of the First International Conference on Analytical and Computational Methods in Probability Theory and its Applications, ACMPT 2017, held in Moscow, Russia, in October 2017. The 42 full papers presented were carefully reviewed and selected from 173 submissions. The conference program consisted of four main themes associated with significant contributions made by A.D.Soloviev. These are: Analytical methods in probability theory, Computational methods in probability theory, Asymptotical methods in probability theory, the history of mathematics.