Dependence modeling and inference for multivariate data

该研究计划涉及随机模型和统计推断过程的发展，用于研究几个随机变量之间的相关性。这一主题在保险、金融或水文领域至关重要，因为在这些领域，对索赔、资产或极端降水之间的依赖性进行会计处理可以带来更好的风险管理实践，并改善公共安全。 用于分析多变量数据的传统工具，例如，回归和时间序列模型通常依赖于变量（或其适当的变换）遵循多变量高斯分布的假设。一种更灵活的方法是直接通过一个称为“copula”的数学对象来对原始变量之间的相关性进行建模。" 当处理连续数据时，Copula允许单独处理随机向量的分量之间的依赖性和边缘分布。它们不仅可以比较不同边际的多变量总体之间的依赖程度，还可以比较它们之间的依赖性质。为了实现这一目标，并确保结论对边际分布的误设定具有鲁棒性，Copula的估计量和拟合优度检验通常基于秩。 赠款保持器持有人自1985年以来一直是该领域的贡献者，并将继续沿着类似的路线进行研究，特别是通过为涉及大量变量的情况开发copula模型，并将基于等级的推理技术适用于具体的依赖结构（例如，阿基米德、极值或亚椭圆）或离散、混合或依赖于时间或其他协变量的数据。

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.