Elements of copula modeling with R
著者
書誌事項
Elements of copula modeling with R
（Use R! / series editors, Robert Gentleman, Kurt Hornik, Giovanni Parmigiani）
Springer, c2018
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
Preface 51 Introduction 91.1 A motivating example . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2 Probability and quantile transformations . . . . . . . . . . . . . . . . . 111.3 Copulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4 Structure and philosophy of the book . . . . . . . . . . . . . . . . . . . 141.5 Additional references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 Copulas 172.1 Denition and characterization . . . . . . . . . . . . . . . . . . . . . . 172.2 The Frechet{Hoeding bounds . . . . . . . . . . . . . . . . . . . . . . . 272.3 Sklar's Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.4 The invariance principle . . . . . . . . . . . . . . . . . . . . . . . . . . 442.5 Survival copulas and copula symmetries . . . . . . . . . . . . . . . . . 492.6 Measures of association . . . . . . . . . . . . . . . . . . . . . . . . . . . 542.6.1 Fallacies related to the correlation coecient . . . . . . . . . . . 552.6.2 Rank correlation measures . . . . . . . . . . . . . . . . . . . . . 602.6.3 Tail dependence coecients . . . . . . . . . . . . . . . . . . . . . 672.7 Rosenblatt transform and conditional sampling . . . . . . . . . . . . . 763 Classes and families 873.1 Elliptical distributions and copulas . . . . . . . . . . . . . . . . . . . . 873.1.1 Elliptical distributions . . . . . . . . . . . . . . . . . . . . . . . . 873.1.2 Elliptical copulas . . . . . . . . . . . . . . . . . . . . . . . . . . 923.2 Archimedean copulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023.3 Extreme-value copulas . . . . . . . . . . . . . . . . . . . . . . . . . . . 1163.4 Selected copula transformations and constructions . . . . . . . . . . . . 1223.4.1 Rotated copulas . . . . . . . . . . . . . . . . . . . . . . . . . . . 1223.4.2 Khoudraji's device . . . . . . . . . . . . . . . . . . . . . . . . . . 1263.4.3 Mixtures of copulas . . . . . . . . . . . . . . . . . . . . . . . . . 1324 Estimation 1374.1 Estimation under a parametric assumption on the copula . . . . . . . . 1374.1.1 Parametrically estimated margins . . . . . . . . . . . . . . . . . 1384.1.2 Non-parametrically estimated margins . . . . . . . . . . . . . . . 1424.1.3 Estimators of elliptical copula parameters . . . . . . . . . . . . . 1514.1.4 Other semi-parametric estimators . . . . . . . . . . . . . . . . . 1564.1.5 Estimation of copula models with partly xed parameters . . . . 1564.2 Non-parametric estimation of the copula . . . . . . . . . . . . . . . . . 1614.2.1 The empirical copula . . . . . . . . . . . . . . . . . . . . . . . . 1614.2.2 Under extreme-value dependence . . . . . . . . . . . . . . . . . . 1645 Graphical diagnostics, tests and model selection 1675.1 Basic graphical diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . 1675.2 Hypothesis tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1735.2.1 Tests of independence . . . . . . . . . . . . . . . . . . . . . . . . 1735.2.2 Tests of exchangeability . . . . . . . . . . . . . . . . . . . . . . . 1755.2.3 A test of radial symmetry . . . . . . . . . . . . . . . . . . . . . . 1775.2.4 Tests of extreme-value dependence . . . . . . . . . . . . . . . . . 1785.2.5 Goodness-of-t tests . . . . . . . . . . . . . . . . . . . . . . . . . 1815.2.6 A mixture of graphical and formal goodness-of-t tests . . . . . 1885.3 Model selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1896 Ties, time series and regression 1956.1 Ties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1966.2 Selected copula tests and models for time series . . . . . . . . . . . . . 2146.2.1 Tests of stationarity . . . . . . . . . . . . . . . . . . . . . . . . . 2146.2.2 Tests of serial independence . . . . . . . . . . . . . . . . . . . . 2256.2.3 Models for multivariate time series based on conditional copulas 2296.3 Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235A R and package versions 251References 255Index 267
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