Dependence Modeling With Copulas

Statistics The author shows how numerical methods and algorithms for inference and simulation are important in high-dimensional copula applications. He presents the algorithms as pseudocode, illustrating their implementation for high-dimensional copula models. He also incorporates results to determine dependence and tail properties of multivariate distributions for future constructions of copula models. Features • Explores a variety of applications of dependence modeling with copulas • Compares copula families and constructions with many kinds of dependence structures and tail properties • Explains how the properties affect tail inferences, such as joint tail probabilities and tail conditional expectations • Describes novel vine copula techniques for modeling high-dimensional data • Covers inference, diagnostics, model selection, numerical methods, and algorithms for copula applications • Includes some theoretical details and advanced examples • Offers software and code on the author’s website Monographs on Statistics and Applied Probability 134 Dependence Modeling with Copulas Dependence Modeling with Copulas covers the substantial advances that have taken place in the field during the last 15 years, including vine copula modeling of high-dimensional data. Vine copula models are constructed from a sequence of bivariate copulas. The book develops generalizations of vine copula models, including common and structured factor models that extend from the Gaussian assumption to copulas. It also discusses other multivariate constructions and parametric copula families that have different tail properties and presents extensive material on dependence and tail properties to assist in copula model selection. 134 Dependence Modeling with Copulas Joe K18978 K18978_cover.indd 1 Harry Joe 5/21/14 10:46 AM Dependence Modeling with Copulas K18978_FM.indd 1 5/28/14 1:05 PM MONOGRAPHS ON STATISTICS AND APPLIED PROBABILITY General Editors F. Bunea, V. Isham, N. Keiding, T. Louis, R. L. Smith, and H. Tong 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. K18978_FM.indd 2 Stochastic Population Models in Ecology and Epidemiology M.S. Barlett (1960) Queues D.R. Cox and W.L. Smith (1961) Monte Carlo Methods J.M. Hammersley and D.C. Handscomb (1964) The Statistical Analysis of Series of Events D.R. Cox and P.A.W. Lewis (1966) Population Genetics W.J. Ewens (1969) Probability, Statistics and Time M.S. Barlett (1975) Statistical Inference S.D. Silvey (1975) The Analysis of Contingency Tables B.S. Everitt (1977) Multivariate Analysis in Behavioural Research A.E. Maxwell (1977) Stochastic Abundance Models S. Engen (1978) Some Basic Theory for Statistical Inference E.J.G. Pitman (1979) Point Processes D.R. Cox and V. Isham (1980) Identification of Outliers D.M. Hawkins (1980) Optimal Design S.D. Silvey (1980) Finite Mixture Distributions B.S. Everitt and D.J. Hand (1981) Classification A.D. Gordon (1981) Distribution-Free Statistical Methods, 2nd edition J.S. Maritz (1995) Residuals and Influence in Regression R.D. Cook and S. Weisberg (1982) Applications of Queueing Theory, 2nd edition G.F. Newell (1982) Risk Theory, 3rd edition R.E. Beard, T. Pentikäinen and E. Pesonen (1984) Analysis of Survival Data D.R. Cox and D. Oakes (1984) An Introduction to Latent Variable Models B.S. Everitt (1984) Bandit Problems D.A. Berry and B. Fristedt (1985) Stochastic Modelling and Control M.H.A. Davis and R. Vinter (1985) The Statistical Analysis of Composition Data J. Aitchison (1986) Density Estimation for Statistics and Data Analysis B.W. Silverman (1986) Regression Analysis with Applications G.B. Wetherill (1986) Sequential M