Multivariate Interval-Valued Models in Frequentist and Bayesian Schemes

TL;DR

This paper extends interval-valued data analysis to multivariate cases, deriving ML estimators, establishing their distributions, and developing a Bayesian framework, validated through simulations and real data.

Contribution

It introduces the first multivariate interval-valued models in both frequentist and Bayesian schemes, expanding beyond prior univariate focus.

Findings

Derived maximum likelihood estimators for multivariate interval data.

Established asymptotic distributions for the estimators.

Validated estimators through simulations and real-world data analysis.

Abstract

In recent years, addressing the challenges posed by massive datasets has led researchers to explore aggregated data, particularly leveraging interval-valued data, akin to traditional symbolic data analysis. While much recent research, with the exception of Samdai et al. (2023) who focused on the bivariate case, has primarily concentrated on parameter estimation in single-variable scenarios, this paper extends such investigations to the multivariate domain for the first time. We derive maximum likelihood (ML) estimators for the parameters and establish their asymptotic distributions. Additionally, we pioneer a theoretical Bayesian framework, previously confined to the univariate setting, for multivariate 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.