Multivariate Dependence Modeling with Copulas

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The proposed research focuses on new statistical methodology for copula-based dependence models, which are now widely used in many fields, including environmental and health sciences, finance, insurance, and risk management. Dependence in multivariate data is a complex phenomenon and copula-based models are far more capable of accounting for it than traditional multivariate distributions. My research program is a continuation of my previous NSERC Discovery Grant, with a new focus on complex data structures and recent challenges in applications, such as high-dimensional data, discontinuous variables, or low-probability, high-impact events. There is a pressing need for versatile yet tractable multivariate copula models that are well suited for the treatment of high-dimensional data. I will devise such models using stochastic representations, develop statistical methodology for them, and make this new methodology available to end-users of statistics through the R Project for Statistical Computing. I will also use the new models to build hierarchical dependence structures for clustered data. Another part of my research will focus on the modeling of dependence between extreme events: I will develop novel statistical techniques based on constrained B-spline estimation; the estimators will correspond to genuine models from which it is possible to simulate and predict catastrophic events. Moreover, I will further my work on empirical copula processes for non-continuous data. This work will serve as a basis for valid statistical methodology for copula-based models for variables that are discrete, mixed or otherwise discontinuous. These new techniques will also be investigated in settings where the number of variables is large; the aim will be to devise graphical tools for the visualization of dependence in high-dimensional data. My methodological work will be applied to various practical problems, e.g., in hydrology, insurance, and risk management. The impact of the work will be to change the manner in which researchers model multivariate data. It will demonstrate the usefulness of copula-based techniques, and its feasibility even for complex data structures. The research will contribute to the growing literature on high-dimensional dependence modeling, which is of interest to a wide statistical audience. Given the importance of dependence-related issues in fields such as finance, insurance, hydrology, and risk management, the work will have parallel impact in these areas. New methodology will be made accessible to practitioners through the R Project for Statistical Computing.