Dependence modeling and inference for multivariate data

该研究项目涉及发展随机模型和统计推理程序，用于研究几个随机变量之间的相关性。这一主题在保险、金融或水文学领域至关重要，因为在这些领域，理赔、资产或极端降水之间的依赖关系会带来更好的风险管理实践，并改善公共安全。

The research program is concerned with the development of stochastic models and statistical inference proce- dures for the study of dependence between several random variables. This topic is of prime importance in insurance, finance or hydrology, where accounting for dependence between claims, assets or extreme precipitations leads to better risk management practices and improves public safety. Traditional tools for analyzing multivariate data, e.g., regression and time series models, generally rely on the hypothesis that the variables (or suitable transformations thereof) follow a multivariate Gaussian distribution. A more flexible approach consists of modeling the dependence between the original variables directly through a mathematical object called a "copula." When dealing with continuous data, copulas allow for a separate treatment of the dependence between, and the marginal distributions of, the components of a random vector. They make it possible to compare not only the degree, but also the nature of dependence between multivariate populations with distinct margins. To accom- plish this goal and ensure that conclusions are robust to misspecification of the marginal distributions, estimators and goodness-of-fit tests for copulas are typically based on ranks. The grant holder has been a contributor to the area since 1985 and will pursue his research along similar lines, notably through the development of copula models for situations involving a large number of variables and the adaptation of rank-based inference techniques to specific dependence structures (e.g., Archimedean, extreme- value, or meta-elliptical) or to data that are either discrete, mixed, or dependent on time or other covariates.