Multivariate Box-Cox symmetric models generated by a normal scale mixture copula - Medeiros, Rodrigo Matheus Rocha de (2024)
The class of the Box-Cox symmetric distributions offers a flexible modeling framework for positive continuous data, reaching different levels of skewness and tail-heaviness. However, this class has been little explored in dependence modeling. The copula theory provides an approach for modeling dependence through a function that characterizes the associations among the elements of a random vector with given marginals. For instance, copulas generated by scale mixtures of normal distributions have attractive properties and describe dependence similarly to the multivariate normal distribution. This thesis aims to introduce a broad class of multivariate probability distributions and associated multivariate and marginal regression models. The class has Box-Cox symmetric marginal distributions, while a copula of a scale mixture of normal distributions describes the dependence structure. The models studied in this thesis constitute a general and flexible framework for modeling positive continuous data, handling from independent data to multivariate data with general forms of dependence. We derive properties and provide interpretations about the copula-induced dependence structure in the class of models. We propose a likelihood-based inference for parameter estimation and discuss a strategy for selecting model components in practical applications. We present simulation studies to verify the performance of the maximum likelihood estimators in finite-sized samples and apply the models to real data sets with different structures.