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.

翻译：近年来，为应对大规模数据集带来的挑战，研究者开始探索聚合数据，特别是利用区间值数据（类似于传统符号数据分析）的方法。尽管近期多数研究（除Samdai等人（2023）聚焦于双变量情形外）主要集中于单变量场景下的参数估计，本文首次将此类研究拓展至多元领域。我们推导了参数的极大似然（ML）估计量并建立了其渐近分布。此外，我们开创性地将此前局限于单变量设置的理论贝叶斯框架应用于多元数据。我们详细阐述了所提出的估计量并进行了性能对比分析。最后，通过仿真实验和真实数据分析验证了估计量的有效性。