一种带有矩阵负二项稀疏的新型矩阵值整数自回归过程
A new matrix-variate integer-valued autoregressive process with matrical negative binomial thinning
AI总结：
本文针对矩阵值整数时间序列的过度离散问题，提出带矩阵负二项稀疏的新型整数自回归模型，开发两种估计方法并验证其性能，该模型拟合效果优于两类对比模型。
AI中文摘要：
针对社会学、医学及相关领域中矩阵值整数时间序列数据的过度离散问题，本文提出一种基于负二项稀疏算子的矩阵值整数自回归模型。通过引入左右矩阵负二项稀疏算子，所提模型既保留了数据的整数特性，又能有效处理过度离散问题。本文系统研究了该模型的概率与统计性质，开发了投影估计和迭代条件最小二乘估计两种估计方法，并建立了相应的渐近理论。模拟研究提供了具体数值结果以评估估计量的有限样本性能，实证数据分析表明，所提模型在拟合矩阵值整数时间序列时，性能优于连续矩阵自回归模型和多元整数自回归模型，且在容纳过度离散计数数据方面也被证明是有效的。
英文摘要：
To address the overdispersion problem in matrix-variate integer-valued time series data arising in sociology, medicine, and related fields, this paper proposes a matrix integer-valued autoregressive model based on the negative binomial thinning operator. By introducing left and right matricial negative binomial thinning operators, the proposed model not only preserves the integer-valued nature of the data but also effectively handles overdispersion. The probabilistic and statistical properties of the proposed model are systematically investigated. Two estimation methods, namely projection estimation and iterative conditional least squares estimation are developed, and the corresponding asymptotic theories are established. Simulation studies provide concrete numerical results to evaluate the finite-sample performance of the estimators. Real data analysis demonstrates that the proposed model outperforms both the continuous matrix autoregressive model and the multivariate integer-valued autoregressive model in fitting matrix-variate integer-valued time series, while also proving effective in accommodating overdispersed count data.
