Elements of Copula Modeling with R

This book introduces the main theoretical findings related to copulas and shows how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment with the package copula (among others).

Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling dependence among random variables in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, and meteorology, to name a few.

In the spirit of the Use R! series, each chapter combines key theoretical definitions or results with illustrations in R. Aimed at statisticians, actuaries, risk managers, engineers and environmental scientists wanting to learn about the theory and practice of copula modeling using R without an overwhelming amount of mathematics, the book can also be used for teaching a course on copula modeling.

Offers an introduction to copulas and their main properties, along with the most important theoretical results Illustrates the concepts using stand-alone and reproducible R examples involving synthetic or real-world data Elaborates copula transformations, copula estimation, graphical diagnostics, statistical tests and model selection Addresses advanced topics such as the handling of ties, time series and covariates in a regression setting

Auteur
The four authors of the book are the authors of the R package copula available on CRAN.

Marius Hofert is an assistant professor of statistics at the University of Waterloo, Canada. He obtained his Ph.D. in mathematics from the University of Ulm, Germany in 2010. He then held a postdoctoral research position at ETH Zurich, Switzerland. After guest assistant professorships at the Technical University Munich, Germany and the University of Washington, USA, he joined the Department of Statistics and Actuarial Science at the University of Waterloo in 2014. His main research interests lie in copula modeling, computational statistics, data science and quantitative risk management.

Ivan Kojadinovic is a professor of statistics at the University of Pau, France. He received his Ph.D. from the University of Reunion, France in 2002 and joined the University of Nantes, France in 2003 as an assistant professor. From 2007 to 2010, he was a lecturer and then a senior lecturer at the Department of Statistics of the University of Auckland, New Zealand, before joining the University of Pau in 2010. His research interests lie in nonparametric statistics, copulas, change-point detection, and environmental and financial applications.

Martin Mächler is a lecturer and senior scientist at the ETH Zurich, Switzerland. He received his Ph.D. in mathematics from the ETH in 1989, and spent his postdoc years at the University of Washington, Seattle and Bell Communications Research (Bellcore), before joining the Seminar für Statistik at the ETH as lecturer in 1991. He became involved with R in 1995, was a founding member of the R core team in 1997 and has since been active in the development of R. His research interests include nonparametric curve estimation, numerical approximation, clustering, robust statistics, sparse matrices and statistical computing in general. He has been the maintainer of circa 20 CRAN R packages, including the "recommended" packages Matrix and cluster.

Jun Yan is a professor of statistics at the University of Connecticut, USA. He received his Ph.D. in statistics from University of Wisconsin - Madison, USA in 2003. He was an assistant professor at the University of Iowa, USA before joining UConn in 2007. His research interests include survival analysis, clustered data analysis, multivariate dependence, spatial extremes, and statistical computing. Actively involved in collaborative research in public health and environmental sciences, he has a special interest in making advanced statistical methods widely accessible via open source software.

Contenu
Preface.- Introduction.- Copulas.- Classes and Families.- Estimation.- Graphical Diagnostics, Tests and Model Selection.- Ties, Time Series and Regression.- R and Package Versions.- References.- Index.