Ebook: Extreme Value Theory: Proceedings of a Conference held in Oberwolfach, Dec. 6–12, 1987

The urgent need to describe and to solve certain problems connected to extreme phenomena in various areas of applications has been of decisive influence on the vital development of extreme value theory. After the pioneering work of M. Frechet (1927) and of R.A. Fisher and L.R.C. Tippett (1928), who discovered the limiting distributions of extremes, the importance of mathematical concepts of extreme behavior in applications was impressively demonstrated by statisticians like E.J. Gumbel and W. Weibull. The predominant role of applied aspects in that early period may be highlighted by the fact that two of the "Fisher-Tippett asymptotes" also carry the names of Gumbel and Weibull. In the last years, the complexity of problems and their tractability by mathematical methods stimulated a rapid development of mathematical theory that substantially helped to improve our understanding of extreme behavior. Due to the depth and richness of mathematical ideas, extreme value theory has become more and more of interest for mathematically oriented research workers. This was one of the reasons to organize a conference on extreme value theory which was held at the Mathematische Forschungsinstitut at Oberwolfach (FRG) in December 1987.

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The theory of extreme values has become a broad subject which is difficult to cover by a few authors. It is the purpose of this book to lay out in an expository way the broad spectrum of extremes by contributions, some of which are reviewing recent developments and some are including original ideas and results. In the last years, the complexity of problems and their tractability by mathematical methods stimulated a rapid development of mathematical theory that substantially helped to improve our understanding of extreme behavior. Due to the depth and richness of mathematical ideas, extreme value theory has become more and more interesting to mathematically oriented research workers. This was one of the reasons a conference on extreme value theory was held at the Mathematische Forschungsinstitut at Oberwolfach (FRG) in December 1987. The book is split into three parts with a total number of nine sections. The topics covered include probabilistic theory, statistical theory of extreme values, and multivariate extremes and records.

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The theory of extreme values has become a broad subject which is difficult to cover by a few authors. It is the purpose of this book to lay out in an expository way the broad spectrum of extremes by contributions, some of which are reviewing recent developments and some are including original ideas and results. In the last years, the complexity of problems and their tractability by mathematical methods stimulated a rapid development of mathematical theory that substantially helped to improve our understanding of extreme behavior. Due to the depth and richness of mathematical ideas, extreme value theory has become more and more interesting to mathematically oriented research workers. This was one of the reasons a conference on extreme value theory was held at the Mathematische Forschungsinstitut at Oberwolfach (FRG) in December 1987. The book is split into three parts with a total number of nine sections. The topics covered include probabilistic theory, statistical theory of extreme values, and multivariate extremes and records.
Content:
Front Matter....Pages I-X
Best Attainable Rate of Joint Convergence of Extremes....Pages 1-9
Recent Results on Asymptotic Expansions in Extreme Value Theory....Pages 10-20
Simple Estimators of the Endpoint of a Distribution....Pages 132-147
Asymptotic Normality of Hill’s Estimator....Pages 148-155
Extended Extreme Value Models and Adaptive Estimation of the Tail Index....Pages 156-165
Asymptotic Results for an Extreme Value Estimator of the Autocorrelation Coefficient for a First Order Autoregressive Sequence....Pages 166-180
Strong Laws for the k-th Order Statistic when k ? c log2n (II)....Pages 21-35
Extreme Values with Very Heavy Tails....Pages 36-49
The Selection of the Domain of Attraction of an Extreme Value Distribution from a Set of Data....Pages 181-190
Comparison of Extremal Models through Statistical Choice in Multidimensional Backgrounds....Pages 191-203
Strong Laws for the k-th Order Statistic when k ? c log2n (II)....Pages 21-35
A Survey on Strong Approximation Techniques in Connection with Records....Pages 50-58
Self-Similar Random Measures, their Carrying Dimension, and Application to Records....Pages 59-68
The Role of Extreme Order Statistics for Exponential Families....Pages 204-221
Extreme Values with Very Heavy Tails....Pages 36-49
On Exceedance Point Processes for Stationary Sequences under Mild Oscillation Restrictions....Pages 69-80
A Central Limit Theorem for Extreme Sojourn Times of Stationary Gaussian Processes....Pages 81-99
On the Distribution of Random Waves and Cycles....Pages 100-113
Characterizations of the Exponential Distribution by Failure Rate- and Moment Properties of Order Statistics....Pages 114-124
A Characterization of the Uniform Distribution via Maximum Likelihood Estimation of its Location Parameter....Pages 125-131
Simple Estimators of the Endpoint of a Distribution....Pages 132-147
Asymptotic Normality of Hill’s Estimator....Pages 148-155
Extended Extreme Value Models and Adaptive Estimation of the Tail Index....Pages 156-165
Asymptotic Results for an Extreme Value Estimator of the Autocorrelation Coefficient for a First Order Autoregressive Sequence....Pages 166-180
The Selection of the Domain of Attraction of an Extreme Value Distribution from a Set of Data....Pages 181-190
Comparison of Extremal Models through Statistical Choice in Multidimensional Backgrounds....Pages 191-203
The Role of Extreme Order Statistics for Exponential Families....Pages 204-221
Multivariate Records and Shape....Pages 222-233
Limit Distributions of Multivariate Extreme Values in Nonstationary Sequences of Random Vectors....Pages 234-245
Statistical Decision for Bivariate Extremes....Pages 246-261
Multivariate Negative Exponential and Extreme Value Distributions....Pages 262-274
Back Matter....Pages 275-279

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The theory of extreme values has become a broad subject which is difficult to cover by a few authors. It is the purpose of this book to lay out in an expository way the broad spectrum of extremes by contributions, some of which are reviewing recent developments and some are including original ideas and results. In the last years, the complexity of problems and their tractability by mathematical methods stimulated a rapid development of mathematical theory that substantially helped to improve our understanding of extreme behavior. Due to the depth and richness of mathematical ideas, extreme value theory has become more and more interesting to mathematically oriented research workers. This was one of the reasons a conference on extreme value theory was held at the Mathematische Forschungsinstitut at Oberwolfach (FRG) in December 1987. The book is split into three parts with a total number of nine sections. The topics covered include probabilistic theory, statistical theory of extreme values, and multivariate extremes and records.
Content:
Front Matter....Pages I-X
Best Attainable Rate of Joint Convergence of Extremes....Pages 1-9
Recent Results on Asymptotic Expansions in Extreme Value Theory....Pages 10-20
Simple Estimators of the Endpoint of a Distribution....Pages 132-147
Asymptotic Normality of Hill’s Estimator....Pages 148-155
Extended Extreme Value Models and Adaptive Estimation of the Tail Index....Pages 156-165
Asymptotic Results for an Extreme Value Estimator of the Autocorrelation Coefficient for a First Order Autoregressive Sequence....Pages 166-180
Strong Laws for the k-th Order Statistic when k ? c log2n (II)....Pages 21-35
Extreme Values with Very Heavy Tails....Pages 36-49
The Selection of the Domain of Attraction of an Extreme Value Distribution from a Set of Data....Pages 181-190
Comparison of Extremal Models through Statistical Choice in Multidimensional Backgrounds....Pages 191-203
Strong Laws for the k-th Order Statistic when k ? c log2n (II)....Pages 21-35
A Survey on Strong Approximation Techniques in Connection with Records....Pages 50-58
Self-Similar Random Measures, their Carrying Dimension, and Application to Records....Pages 59-68
The Role of Extreme Order Statistics for Exponential Families....Pages 204-221
Extreme Values with Very Heavy Tails....Pages 36-49
On Exceedance Point Processes for Stationary Sequences under Mild Oscillation Restrictions....Pages 69-80
A Central Limit Theorem for Extreme Sojourn Times of Stationary Gaussian Processes....Pages 81-99
On the Distribution of Random Waves and Cycles....Pages 100-113
Characterizations of the Exponential Distribution by Failure Rate- and Moment Properties of Order Statistics....Pages 114-124
A Characterization of the Uniform Distribution via Maximum Likelihood Estimation of its Location Parameter....Pages 125-131
Simple Estimators of the Endpoint of a Distribution....Pages 132-147
Asymptotic Normality of Hill’s Estimator....Pages 148-155
Extended Extreme Value Models and Adaptive Estimation of the Tail Index....Pages 156-165
Asymptotic Results for an Extreme Value Estimator of the Autocorrelation Coefficient for a First Order Autoregressive Sequence....Pages 166-180
The Selection of the Domain of Attraction of an Extreme Value Distribution from a Set of Data....Pages 181-190
Comparison of Extremal Models through Statistical Choice in Multidimensional Backgrounds....Pages 191-203
The Role of Extreme Order Statistics for Exponential Families....Pages 204-221
Multivariate Records and Shape....Pages 222-233
Limit Distributions of Multivariate Extreme Values in Nonstationary Sequences of Random Vectors....Pages 234-245
Statistical Decision for Bivariate Extremes....Pages 246-261
Multivariate Negative Exponential and Extreme Value Distributions....Pages 262-274
Back Matter....Pages 275-279
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