Estimation and model selection for graphical models under mixing conditions

• Ano de defesa: 2024
• Autor(a) principal: Severino, Magno Tairone de Freitas
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Estimação de estruturas de grafo; Estimador regularizado; Mixing processes; Model selection; Processos de mistura; Regularized estimator; Seleção de modelos; Sructure estimation
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45133/tde-25042024-181144/

This thesis introduces a novel approach for estimating the graph of conditional dependencies in a random vector based on finite sample data. We define this approach as a global model selection criterion, which means optimizing a function across the entire set of potential graphs, removing the need to estimate and combine individual neighborhoods as commonly proposed in the literature. Our results establishes the strong convergence of this graph estimator, provided that the multivariate stochastic process satisfies a mixing condition. To the best of our knowledge, these results represent a pioneering demonstration of the consistency of a model selection criterion for Markov random fields on graphs when dealing with non-independent data. Additionally, we propose efficient algorithms for graph estimation and complement our theoretical results with simulation studies. To illustrate the practical applicability of our approach, we present two real-world examples: a study of the dependence structure among water flow measurements gauges located in the course of the S\\~ao Francisco River in Brazil; and a daily stock market index performance analysis in order to identify the conditional dependence among the stock markets around the world.