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Fan, Xinyao

University of British Columbia

Dependence models with copulas are widely used in multivariate applications where the assumption of Gaussian distributed variables does not hold. They are useful tools for dependence modeling as they allow flexible univariate margins and a wide range of dependence structures. Several new research directions are explored with latent variables for high-dimensional dependence modeling. The contributions of the thesis are: (a) Proposing proxies for the latent variables in Gaussian factor and factor copula models and providing a theoretical foundation for proxy variables. (b) Extending the use of proxies to factor copula models with weak residual dependence and demonstrating the robustness of the proxies. (c) Proposing two flexible methods for building vine copula models with latent variables in high dimensions. (d) Applying the proposed approaches to dependence modeling for multiple datasets, including financial returns and gene expression datasets. The proxies are conditional expectations of the latent variables given the observed variables. With mild conditions, the proxies are consistent as the sample size and the number of observed variables linked to each latent variable go to infinity. When the bivariate copulas linking observed variables to latent variables are not assumed in advance, sequential procedures are used for latent variable estimation, copula family selection, and copula parameter estimation. Furthermore, the conditional expectation proxies are applied to the models where there is a slight deviation from the conditional independence assumption in factor models. In a large set of variables that can be grouped such that there are stronger within group dependence and weaker between-group dependence, two flexible approaches are proposed for constructing vine copula models with latent variables. For applications, the proposed approaches are applied to several datasets, demonstrating their effectiveness and interpretability in dependence modeling in high dimensions.

Text

2024-04-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/88133

Statistics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/