Exceedance-based nonlinear regression of tail dependence
- 15 Downloads
The probability and structure of co-occurrences of extreme values in multivariate data may critically depend on auxiliary information provided by covariates. In this contribution, we develop a flexible generalized additive modeling framework based on high threshold exceedances for estimating covariate-dependent joint tail characteristics for regimes of asymptotic dependence and asymptotic independence. The framework is based on suitably defined marginal pretransformations and projections of the random vector along the directions of the unit simplex, which lead to convenient univariate representations of multivariate exceedances based on the exponential distribution. Good performance of our estimators of a nonparametrically designed influence of covariates on extremal coefficients and tail dependence coefficients are shown through a simulation study. We illustrate the usefulness of our modeling framework on a large dataset of nitrogen dioxide measurements recorded in France between 1999 and 2012, where we use the generalized additive framework for modeling marginal distributions and tail dependence in large concentrations observed at pairs of stations. Our results imply asymptotic independence of data observed at different stations, and we find that the estimated coefficients of tail dependence decrease as a function of spatial distance and show distinct patterns for different years and for different types of stations (traffic vs. background).
KeywordsAsymptotic independence Extreme value theory Generalized additive models Penalized likelihood Tail dependence
Mathematics Subject Classification (2010)62G32 . 62H99
Unable to display preview. Download preview PDF.
The authors would like to thank the Editor, the Associate Editor, and two anonymous reviewers for valuable comments and suggestions. Financial support from the Centre de Recherches Mathématiques and the Canadian Statistical Sciences Institute (Linda Mhalla), the French national programme LEFE/INSU (Thomas Opitz), and the Swiss National Science Foundation (Valérie Chavez-Demoulin) is gratefully acknowledged.
- Fougères, A.-L.: Multivariate extremes. In: Finkenstädt, B., Rootzén, H. (eds.) Extreme Values in Finance, Telecommunications, and the Environment. Monographs on Statistics and Applied Probability 99 (2004)Google Scholar
- Hofert, M., Kojadinovic, I., Maechler, M., Yan, J.: Copula: Multivariate Dependence with Copulas. R package version 0.999-18. https://CRAN.R-project.org/package=copula (2017)
- Mhalla, L., De Carvalho, M., Chavez-Demoulin, V.: Regression type models for extremal dependence. arXiv:1704.08447 (2017)
- Nelsen, R.B.: An Introduction to Copulas, Springer Series in Statistics, 2nd edn. Springer, New York (2006)Google Scholar
- Pickands, J.: Multivariate extreme value distributions. In: Proc. 43rd Session of the International Statistical Institute, pp 859–878 (1981)Google Scholar