UBC Theses and Dissertations
Conditional inferences and predictions based on copula models Pan, Shenyi
Copulas combined with univariate distributions are a flexible tool for modeling distributions beyond Gaussian. Vine copulas based on a nested sequence of trees and a sequence of bivariate copulas can be used to construct high-dimensional copula models with flexible dependence structures. A multivariate model based on vine copulas assumes that variables are observed simultaneously in a sample. The contributions of this thesis are the new conditional inference and prediction methods based on vine copulas, including: (a) conditional distribution of one variable given others, (b) conditional distribution when the response variable is right-censored, (c) conditional distribution when some explanatory variables are nominal categorical. For (a), an algorithm is developed to compute arbitrary conditional distributions of one variable given the others for cross prediction from a single joint distribution fitted by vine copulas. An existing algorithm is also modified to simulate data from a vine copula given that one variable takes extreme values. For (b), in time-to-event and survival studies, the goal is to model the right-censored response variable with the explanatory variables to obtain point and interval predictions. The existing vine copula regression methodology is extended with a censored response variable and a set of discrete or continuous explanatory variables. For (c), for a nominal variable with three or more unordered categories, there is a PMF but no CDF. For use within vine copulas, the nominal variable is either converted to an ordinal variable, or encoded as binary dummy variables, similar to other regression models. The existing vine copula regression method is extended to allow some of the explanatory variables to be binary dummy variables with positive dependence converted from nominal variables. When fitting copula models with previous settings, there can be pairs of mixed continuous-discrete variables on the edges of a vine. The existing diagnostic methods for two continuous variables are not valid, and new diagnostic methods are developed. When parametric copula families do not provide adequate fits, nonparametric copulas can be used with adaptations for mixed continuous-ordinal variables. Allowing nonparametric copulas for mixed continuous-ordinal variables can improve the performance of vine copulas when applied to conditional inference.
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