Extreme Value Modeling and Risk Analysis: Methods and Applications presents a broad overview of statistical modeling of extreme events along with the most recent methodologies and various applications. The book brings together background material and advanced topics, eliminating the need to sort through the massive amount of literature on the subject.
After reviewing univariate extreme value analysis and multivariate extremes, the book explains univariate extreme value mixture modeling, threshold selection in extreme value analysis, and threshold modeling of non-stationary extremes. It presents new results for block-maxima of vine copulas, develops time series of extremes with applications from climatology, describes max-autoregressive and moving maxima models for extremes, and discusses spatial extremes and max-stable processes. The book then covers simulation and conditional simulation of max-stable processes; inference methodologies, such as composite likelihood, Bayesian inference, and approximate Bayesian computation; and inferences about extreme quantiles and extreme dependence. It also explores novel applications of extreme value modeling, including financial investments, insurance and financial risk management, weather and climate disasters, clinical trials, and sports statistics.
Risk analyses related to extreme events require the combined expertise of statisticians and domain experts in climatology, hydrology, finance, insurance, sports, and other fields. This book connects statistical/mathematical research with critical decision and risk assessment/management applications to stimulate more collaboration between these statisticians and specialists.
Table of Contents
Univariate Extreme Value Analysis. Multivariate Extreme Value Analysis. Univariate Extreme Value Mixture Modeling. Threshold Selection in Extreme Value Analysis. Threshold Modeling of Nonstationary Extremes. Block-Maxima of Vines. Time Series of Extremes. Max-Autoregressive and Moving Maxima Models for Extremes. Spatial Extremes and Max-Stable Processes. Simulation of Max-Stable Processes. Conditional Simulation of Max-Stable Processes. Composite Likelihood for Extreme Values. Bayesian Inference for Extreme Value Modeling. Modeling Extremes Using Approximate Bayesian Computation. Estimation of Extreme Conditional Quantiles. Extreme Dependence Models. Nonparametric Estimation of Extremal Dependence. An Overview of Nonparametric Tests of Extreme-Value Dependence and of Some Related Statistical Procedures. Extreme Risks of Financial Investments. Interplay of Insurance and Financial Risks with Bivariate Regular Variation. Weather and Climate Disasters. The Analysis of Safety Data from Clinical Trials. Analysis of Bivariate Survival Data Based on Copulas with Log Generalized Extreme Value Marginals. Change Point Analysis of Top Batting Average. Computing Software.
Jun Yan is a professor in the Department of Statistics at the University of Connecticut. He was previously an assistant professor at the University of Iowa. He received a Ph.D. in statistics from the University of Wisconsin–Madison. His research interests include spatial extremes, copulas, survival analysis, estimating equations, clustered data analysis, statistical computing, and applications in public health and environment.
Dipak K. Dey is a Board of Trustees Distinguished Professor in the Department of Statistics and associate dean of the College of Liberal Arts and Sciences at the University of Connecticut. He is an elected fellow of the International Society for Bayesian Analysis and American Association for the Advancement of Science, an elected member of the Connecticut Academy of Arts and Sciences and International Statistical Institute, and a fellow of the American Statistical Association and Institute of Mathematical Statistics. Dr. Dey is a co-editor and co-author of several books, including the Chapman & Hall/CRC Bayesian Modeling in Bioinformatics and A First Course in Linear Model Theory. His research interests include Bayesian analysis, bioinformatics, biostatistics, computational statistics, decision theory, environmental statistics, multivariate analysis, optics, reliability and survival analysis, statistical shape analysis, and statistical genetics.
"This book has a broad readership, and it will be useful to graduate students and researchers in the field of statistics, finances, insurance, economics, geosciences, etc.. . This is an impressive and useful book, one which gives an effective account of statistical methods and theory used in extreme value analysis, as applied to problems arising in a variety of fields. It serves as an excellent, contemporary reference text in the area."
~International Statistical Review (2017)
"The strength of the book is its wide range, and it gives the reader a good idea of extremes’ current vanguard. Appropriately, much of the work in the book focuses on dependence in extremes, whether it be in the multivariate, temporal, or spatial setting. . . A practitioner can use this book to get a good introduction to the current state-of-the-art for their type of problem, and use the relevant chapters and references as a launchpoint for their own study."
~The International Biometric Society