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Inference for Multivariate Interval Data: Bridging Frequentist and Bayesian Paradigms
Inferencia para datos interválicos multivariados: un puente entre los paradigmas frecuentista y bayesiano
DOI:
https://doi.org/10.15446/rce.v49n1.119621Keywords:
Bayesian estimation, Entropy loss, Interval-valued data, L2 loss, Maximum likelihood estimation (en)Datos interválicos, Estimación bayesiana, Estimación por máxima verosimilitud, Pérdida L2, Pérdida por entropía (es)
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In recent years, the challenges posed by massive datasets have led researchers to explore aggregated representations, particularly interval-valued data, within the framework of symbolic data analysis. Although most recent research—apart from Samadi et al. (2024), who focused on the bivariate case—has primarily addressed parameter estimation in univariate settings, this paper extends these investigations to the general multivariate case for the first time. We derive maximum likelihood (ML) estimators for the parameters and establish their asymptotic distributions. Additionally, we develop a theoretical Bayesian framework, previously confined to the univariate setting, and extend it to multivariate interval-valued data. We provide a detailed exposition of the proposed estimators and conduct comparative performance analyses. Finally, we validate the effectiveness of our estimators through simulations and real-world data analysis.
En los últimos años, los desafíos que plantean los conjuntos de datos masivos han llevado a los investigadores a explorar representaciones agregadas, en particular datos interválicos, en el marco del análisis de datos simbólicos. Aunque la investigación más reciente —salvo Samadi et al. (2024), quienes se centraron en el caso bivariado— ha abordado principalmente la estimación de parámetros en contextos univariados, este trabajo extiende por primera vez dichas investigaciones al caso multivariado general. Derivamos estimadores de máxima verosimilitud (MV) para los parámetros y establecemos sus distribuciones asintóticas. Además, desarrollamos un marco bayesiano teórico, previamente restringido al entorno univariado, y lo extendemos a datos interválicos multivariados. Presentamos una exposición detallada de los estimadores propuestos y realizamos análisis comparativos de desempeño. Finalmente, validamos la efectividad de nuestros estimadores mediante simulaciones y análisis de datos reales.
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