标题： 马尔可夫切换多方程张量回归 显示英文标题

标题： Markov Switching Multiple-equation Tensor Regressions

摘要： 我们提出了一种新的灵活张量模型，用于多方程回归，该模型能够考虑潜在的制度变化。 该模型允许动态系数和跨方程变化的多维协变量。 我们假设系数由一个共同的隐藏马尔可夫过程驱动，以解决结构断裂问题，从而增强模型的灵活性并保持简约性。 我们引入了一种新的Soft PARAFAC分层先验，以实现维度缩减，同时保留协变量张量的结构信息。 所提出的先验包括一种新的多向收缩效应，以解决过度参数化问题。 我们发展了理论结果以帮助超参数选择。 开发了一种基于随机扫描Gibbs和反向拟合策略的有效MCMC算法，以提高后验抽样的计算可扩展性。 MCMC算法的正确性从理论上得到了证明，并通过不同参数设置下的数值实验研究了其计算效率。 通过两个原始真实数据分析展示了该模型框架的有效性。 与当前基准Lasso回归相比，所提出的模型表现出优越的性能。 显示英文摘要

摘要： We propose a new flexible tensor model for multiple-equation regression that accounts for latent regime changes. The model allows for dynamic coefficients and multi-dimensional covariates that vary across equations. We assume the coefficients are driven by a common hidden Markov process that addresses structural breaks to enhance the model flexibility and preserve parsimony. We introduce a new Soft PARAFAC hierarchical prior to achieve dimensionality reduction while preserving the structural information of the covariate tensor. The proposed prior includes a new multi-way shrinking effect to address over-parametrization issues. We developed theoretical results to help hyperparameter choice. An efficient MCMC algorithm based on random scan Gibbs and back-fitting strategy is developed to achieve better computational scalability of the posterior sampling. The validity of the MCMC algorithm is demonstrated theoretically, and its computational efficiency is studied using numerical experiments in different parameter settings. The effectiveness of the model framework is illustrated using two original real data analyses. The proposed model exhibits superior performance when compared to the current benchmark, Lasso regression.