Asymptotics For Associated Random Variables
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Asymptotics For Associated Random Variables
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Author : Paulo Eduardo Oliveira
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-11
Asymptotics For Associated Random Variables written by Paulo Eduardo Oliveira and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-11 with Mathematics categories.
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting the theory in a unified way, explaining relations and implications of the results. It will present basic definitions and characterizations, followed by a collection of relevant inequalities. These are then applied to characterize almost sure and weak convergence of sequences of associated variables. It will also cover applications of positive dependence to the characterization of asymptotic results in nonparametric statistics. The book is directed towards researchers in probability and statistics, with particular emphasis on people interested in nonparametric methods. It will also be of interest to graduate students in those areas. The book could also be used as a reference on association in a course covering dependent variables and their asymptotics. As prerequisite, readers should have knowledge of basic probability on the reals and on metric spaces. Some acquaintance with the asymptotics of random functions, such us empirical processes and partial sums processes, is useful but not essential.
Limit Theorems For Associated Random Fields And Related Systems
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Author : Aleksandr Vadimovich Bulinski?
language : en
Publisher: World Scientific
Release Date : 2007
Limit Theorems For Associated Random Fields And Related Systems written by Aleksandr Vadimovich Bulinski? and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications.There are 434 items in the bibliography.The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.).
Asymptotic Behaviour Of Linearly Transformed Sums Of Random Variables
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Author : V. V. Buldygin
language : en
Publisher:
Release Date : 1997-06-30
Asymptotic Behaviour Of Linearly Transformed Sums Of Random Variables written by V. V. Buldygin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-30 with categories.
Asymptotics Of Random Matrices And Related Models
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Author : Alice Guionnet
language : en
Publisher:
Release Date : 2019
Asymptotics Of Random Matrices And Related Models written by Alice Guionnet and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with MATHEMATICS categories.
Probability theory is based on the notion of independence. The celebrated law of large numbers and the central limit theorem describe the asymptotics of the sum of independent variables. However, there are many models of strongly correlated random variables: for instance, the eigenvalues of random matrices or the tiles in random tilings. Classical tools of probability theory are useless to study such models. These lecture notes describe a general strategy to study the fluctuations of strongly interacting random variables. This strategy is based on the asymptotic analysis of Dyson-Schwinger (or loop) equations: the author will show how these equations are derived, how to obtain the concentration of measure estimates required to study these equations asymptotically, and how to deduce from this analysis the global fluctuations of the model. The author will apply this strategy in different settings: eigenvalues of random matrices, matrix models with one or several cuts, random tilings, and several matrices models.
Asymptotics For Associated Random Variables
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Author : Paulo Eduardo Oliveira
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-13
Asymptotics For Associated Random Variables written by Paulo Eduardo Oliveira and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-13 with Mathematics categories.
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting the theory in a unified way, explaining relations and implications of the results. It will present basic definitions and characterizations, followed by a collection of relevant inequalities. These are then applied to characterize almost sure and weak convergence of sequences of associated variables. It will also cover applications of positive dependence to the characterization of asymptotic results in nonparametric statistics. The book is directed towards researchers in probability and statistics, with particular emphasis on people interested in nonparametric methods. It will also be of interest to graduate students in those areas. The book could also be used as a reference on association in a course covering dependent variables and their asymptotics. As prerequisite, readers should have knowledge of basic probability on the reals and on metric spaces. Some acquaintance with the asymptotics of random functions, such us empirical processes and partial sums processes, is useful but not essential.
Limit Theorems For Associated Random Fields And Related Systems
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Author :
language : en
Publisher:
Release Date :
Limit Theorems For Associated Random Fields And Related Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Asymptotics In Statistics
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Author : Lucien Le Cam
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotics In Statistics written by Lucien Le Cam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is the second edition of a coherent introduction to the subject of asymptotic statistics as it has developed over the past 50 years. It differs from the first edition in that it is now more 'reader friendly' and also includes a new chapter on Gaussian and Poisson experiments, reflecting their growing role in the field. Most of the subsequent chapters have been entirely rewritten and the nonparametrics of Chapter 7 have been amplified. The volume is not intended to replace monographs on specialized subjects, but will help to place them in a coherent perspective. It thus represents a link between traditional material - such as maximum likelihood, and Wald's Theory of Statistical Decision Functions -- together with comparison and distances for experiments. Much of the material has been taught in a second year graduate course at Berkeley for 30 years.
The Asymptotic Theory Of Extreme Order Statistics
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Author : János Galambos
language : en
Publisher:
Release Date : 1987
The Asymptotic Theory Of Extreme Order Statistics written by János Galambos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Asymptotic Theory Of Weakly Dependent Random Processes
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Author : Emmanuel Rio
language : en
Publisher: Springer
Release Date : 2017-04-13
Asymptotic Theory Of Weakly Dependent Random Processes written by Emmanuel Rio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-13 with Mathematics categories.
Ces notes sont consacrées aux inégalités et aux théorèmes limites classiques pour les suites de variables aléatoires absolument régulières ou fortement mélangeantes au sens de Rosenblatt. Le but poursuivi est de donner des outils techniques pour l'étude des processus faiblement dépendants aux statisticiens ou aux probabilistes travaillant sur ces processus.
Asymptotic Analysis Of Random Walks
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Author : Aleksandr Alekseevich Borovkov
language : en
Publisher: Cambridge University Press
Release Date : 2008
Asymptotic Analysis Of Random Walks written by Aleksandr Alekseevich Borovkov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Asymptotic expansions categories.
A comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks.