Banca de QUALIFICAÇÃO: MARIA EDUARDA DA CRUZ JUSTINO
Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.DISCENTE: MARIA EDUARDA DA CRUZ JUSTINO
DATA : 27/03/2026
LOCAL: Google Meet - online (https://meet.google.com/ojz-qgic-dcr)
TÍTULO:
Statistical Modeling, Inference and Diagnostic Tools for Doubly Bounded Response Variables
PALAVRAS-CHAVES:
Beta distribution, beta regression, bootstrap, diagnostic analysis, link function, simplex distribution, simplex regression
PÁGINAS: 96
RESUMO:
We introduce statistical inference procedures for a simplex regression model employing a parametric logit-type link in the mean submodel, allowing for data-driven flexibility and potential asymmetry in the response--predictor relationship. We derive closed-form expressions for the model’s log-likelihood, score, and Fisher information, and propose modified model selection criteria tailored to this specification. A score test is developed to determine the link parameter value, and local influence analysis is used to identify atypical observations. Simulation evidence is provided, and the model’s practical utility is illustrated through an application to cross-sectional data on impunity across more than 100 countries, contrasted with a conventional beta regression. The simplex model provides a slightly better fit and, more importantly, yields inferences and predictions that are less sensitive to influential cases. The proposed framework offers a reliable and flexible alternative for modeling doubly-bounded responses in applied research.
Influence diagnostics are essential for evaluating the stability of regression models and detecting data points with disproportionate impact. Classical measures, such as generalized Cook's distance, are tied to the Fisher information matrix, which can limit their applicability and lead to numerical challenges. We propose novel influence diagnostics for beta regression based on distributional distances, focusing on the Hellinger and Wasserstein metrics. Unlike traditional approaches, these measures do not rely on the information matrix, making them broadly applicable and computationally stable. They also provide complementary perspectives: the Hellinger distance combines analytical tractability with invariance properties, while the Wasserstein distance adds geometric interpretability and flexibility through its $p$-parameter. The proposed methods are evaluated with real and simulated data, demonstrating their ability to identify influential observations and highlighting their potential as practical and reliable alternatives to existing diagnostics.
MEMBROS DA BANCA:
Presidente - 1279737 - FRANCISCO CRIBARI NETO
Externo à Instituição - FÁBIO MARIANO BAYER - UFSM
Interno - 1170969 - KLAUS LEITE PINTO VASCONCELLOS