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Extreme Value Theory for Multivariate Stationary Sequences

Extreme Value Theory for Multivariate Stationary Sequences
Author: Tailen Hsing
Publisher:
Total Pages: 52
Release: 1988
Genre: Convergence
ISBN:

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A distributional mixing condition is introduced for stationary sequences of random vectors to study their extremes. For a sequence satisfying the condition, the following topics which concern the weak limit F of properly normalized partial maxima are studied: (1) To obtain characterizations of F. (2) To study a condition under which the partial maxima behave as they would if the sequence were i.i.d. (3) To consider problems in connection with the independence of the margins of F.


Extremes and Related Properties of Random Sequences and Processes

Extremes and Related Properties of Random Sequences and Processes
Author: M. R. Leadbetter
Publisher: Springer Science & Business Media
Total Pages: 344
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461254493

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Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.


Extreme Values In Random Sequences

Extreme Values In Random Sequences
Author: Pavle Mladenović
Publisher: Springer Nature
Total Pages: 287
Release:
Genre:
ISBN: 3031574125

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Dependence Modeling

Dependence Modeling
Author: Harry Joe
Publisher: World Scientific
Total Pages: 370
Release: 2011
Genre: Business & Economics
ISBN: 981429988X

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1. Introduction : Dependence modeling / D. Kurowicka -- 2. Multivariate copulae / M. Fischer -- 3. Vines arise / R.M. Cooke, H. Joe and K. Aas -- 4. Sampling count variables with specified Pearson correlation : A comparison between a naive and a C-vine sampling approach / V. Erhardt and C. Czado -- 5. Micro correlations and tail dependence / R.M. Cooke, C. Kousky and H. Joe -- 6. The Copula information criterion and Its implications for the maximum pseudo-likelihood estimator / S. Gronneberg -- 7. Dependence comparisons of vine copulae with four or more variables / H. Joe -- 8. Tail dependence in vine copulae / H. Joe -- 9. Counting vines / O. Morales-Napoles -- 10. Regular vines : Generation algorithm and number of equivalence classes / H. Joe, R.M. Cooke and D. Kurowicka -- 11. Optimal truncation of vines / D. Kurowicka -- 12. Bayesian inference for D-vines : Estimation and model selection / C. Czado and A. Min -- 13. Analysis of Australian electricity loads using joint Bayesian inference of D-vines with autoregressive margins / C. Czado, F. Gartner and A. Min -- 14. Non-parametric Bayesian belief nets versus vines / A. Hanea -- 15. Modeling dependence between financial returns using pair-copula constructions / K. Aas and D. Berg -- 16. Dynamic D-vine model / A. Heinen and A. Valdesogo -- 17. Summary and future directions / D. Kurowicka


Extreme Value Theory for Suprema of Random Variables with Regularly Varying Tail Probabilities

Extreme Value Theory for Suprema of Random Variables with Regularly Varying Tail Probabilities
Author: Tailen Hsing
Publisher:
Total Pages: 13
Release: 1986
Genre:
ISBN:

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Extreme value theory concerns the joint tail behavior and related problems of random variables (r.v.'s). Recent emphasis has been the extension of the classical theory, which considers independent and identically distributed (i.i.d.) r.v.'s to the more general setting of stationarity. Progress has been made on topics such as notions of asymptotic independence, general extremal types theorems, studies of related point processes, etc. The author is interested in the extremal properties of stationary sequences whose members are certain functions of i.i.d. r.v.'s. In this direction, previous documents investigated moving average sequences under various assumptions. Through the particular structure of the sequences, these studies provided invaluable insights into the theory in general. This paper considers a stationary sequences (X sub j) consisting of the seighted suprema -- instead of sums as in the case of moving average -- of certain i.i.d. r.v.'s whose tail probabilities are regularly varying. A sequence with this structure may be used to model random exchanges and is a useful tool in studying multivariate extreme value theory.


Extreme Value Theory and Applications

Extreme Value Theory and Applications
Author: J. Galambos
Publisher: Springer Science & Business Media
Total Pages: 526
Release: 2013-12-01
Genre: Mathematics
ISBN: 1461336384

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It appears that we live in an age of disasters: the mighty Missis sippi and Missouri flood millions of acres, earthquakes hit Tokyo and California, airplanes crash due to mechanical failure and the seemingly ever increasing wind speeds make the storms more and more frightening. While all these may seem to be unexpected phenomena to the man on the street, they are actually happening according to well defined rules of science known as extreme value theory. We know that records must be broken in the future, so if a flood design is based on the worst case of the past then we are not really prepared against floods. Materials will fail due to fatigue, so if the body of an aircraft looks fine to the naked eye, it might still suddenly fail if the aircraft has been in operation over an extended period of time. Our theory has by now penetrated the so cial sciences, the medical profession, economics and even astronomy. We believe that our field has come of age. In or~er to fully utilize the great progress in the theory of extremes and its ever increasing acceptance in practice, an international conference was organized in which equal weight was given to theory and practice. This book is Volume I of the Proceedings of this conference. In selecting the papers for Volume lour guide was to have authoritative works with a large variety of coverage of both theory and practice.


An Introduction to Statistical Modeling of Extreme Values

An Introduction to Statistical Modeling of Extreme Values
Author: Stuart Coles
Publisher: Springer Science & Business Media
Total Pages: 219
Release: 2013-11-27
Genre: Mathematics
ISBN: 1447136756

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Directly oriented towards real practical application, this book develops both the basic theoretical framework of extreme value models and the statistical inferential techniques for using these models in practice. Intended for statisticians and non-statisticians alike, the theoretical treatment is elementary, with heuristics often replacing detailed mathematical proof. Most aspects of extreme modeling techniques are covered, including historical techniques (still widely used) and contemporary techniques based on point process models. A wide range of worked examples, using genuine datasets, illustrate the various modeling procedures and a concluding chapter provides a brief introduction to a number of more advanced topics, including Bayesian inference and spatial extremes. All the computations are carried out using S-PLUS, and the corresponding datasets and functions are available via the Internet for readers to recreate examples for themselves. An essential reference for students and researchers in statistics and disciplines such as engineering, finance and environmental science, this book will also appeal to practitioners looking for practical help in solving real problems. Stuart Coles is Reader in Statistics at the University of Bristol, UK, having previously lectured at the universities of Nottingham and Lancaster. In 1992 he was the first recipient of the Royal Statistical Society's research prize. He has published widely in the statistical literature, principally in the area of extreme value modeling.


An Introduction to Statistical Modeling of Extreme Values

An Introduction to Statistical Modeling of Extreme Values
Author: Stuart Coles
Publisher: Springer Science & Business Media
Total Pages: 226
Release: 2001-08-20
Genre: Mathematics
ISBN: 1852334592

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Directly oriented towards real practical application, this book develops both the basic theoretical framework of extreme value models and the statistical inferential techniques for using these models in practice. Intended for statisticians and non-statisticians alike, the theoretical treatment is elementary, with heuristics often replacing detailed mathematical proof. Most aspects of extreme modeling techniques are covered, including historical techniques (still widely used) and contemporary techniques based on point process models. A wide range of worked examples, using genuine datasets, illustrate the various modeling procedures and a concluding chapter provides a brief introduction to a number of more advanced topics, including Bayesian inference and spatial extremes. All the computations are carried out using S-PLUS, and the corresponding datasets and functions are available via the Internet for readers to recreate examples for themselves. An essential reference for students and researchers in statistics and disciplines such as engineering, finance and environmental science, this book will also appeal to practitioners looking for practical help in solving real problems. Stuart Coles is Reader in Statistics at the University of Bristol, UK, having previously lectured at the universities of Nottingham and Lancaster. In 1992 he was the first recipient of the Royal Statistical Society's research prize. He has published widely in the statistical literature, principally in the area of extreme value modeling.