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Abstract: Copulas are multivariate models that allow the modeling of dependence between variables without restrictions on marginal distributions. Copulas are useful for capturing complex dependence properties such as tail dependence, asymmetry, and nonlinearity. The vine copula can be viewed as an extension of a Gaussian copula after the correlation matrix is reparameterized to a set of algebraically independent correlations and partial correlations. It can be used to construct high-dimensional copula models with flexible dependence structures.
We propose extensions to conditional inference and prediction methods based on vine copula models. For conditional inference, an algorithm is developed to compute arbitrary conditional distributions of one variable given the other variables for cross-prediction from a single joint distribution fitted by vine copula models. An existing algorithm is also modified to simulate data from a vine copula given that one variable takes extreme values. To predict a right-censored time-to-event response, a vine copula regression model is fitted to the response variable with the explanatory variables. Existing vine copula regression algorithms are modified to provide point and interval predictions for the censored response.