Modelos skew-normal matriciais e skew-normal matriciais censurados: teoria, inferência e estimação via ECM

Abstract

This thesis develops a comprehensive framework for modeling asymmetric dependence structures in matrix-valued data using the Matrix-Variate Skew-Normal (MVSN) distribution and its censored extension. We establish key theoretical properties of these models, including their stochastic representations, moments, and identifiability conditions. Building on these foundations, we derive likelihood-based inference procedures and propose Expectation–Conditional Maximization (ECM) algorithms capable of handling both fully observed and interval-censored or partially missing matrix-valued observations. Simulation studies are conducted to assess parameter recovery, convergence behavior, and robustness of the proposed estimation methods under diverse scenarios. Finally, we demonstrate the practical usefulness of the models through applications to real datasets with complex censoring structures. The results show that the MVSN and censored MVSN models offer flexible and interpretable tools for analyzing multivariate and matrix-structured data exhibiting asymmetry, moderate tails, and incomplete information.