张量因子模型估计的迭代投影方法
Tensor Factor Model Estimation by Iterative Projection
AI总结：
本文提出两种基于迭代正交投影的张量因子模型估计方法，显著提升估计精度与收敛速度，并推导下界证明最优性。
摘要：
张量时间序列，即由张量观测组成的时间序列，已变得无处不在。它通常表现出高维性。降维的一种方法是使用因子模型结构，其形式类似于Tucker张量分解，但时间维度被处理为具有时间依赖结构的动态过程。在本文中，我们引入了两种通过迭代正交投影原始张量时间序列来估计此类张量因子模型的方法。这些方法扩展了现有的估计程序，并在我们的理论研究中证明了显著提高了估计精度和收敛速度。我们的算法类似于用于张量分解的高阶正交投影方法，但由于迭代中需要展开张量以及使用自相关，存在显著差异。因此，我们的分析与现有分析显著不同。我们推导了计算和统计下界，以证明所提出方法在样本量需求和收敛速度上的最优性。进行了模拟研究以进一步说明这些估计量的统计性质。
英文摘要：
Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to Tucker tensor decomposition, except that the time dimension is treated as a dynamic process with a time dependent structure. In this paper we introduce two approaches to estimate such a tensor factor model by using iterative orthogonal projections of the original tensor time series. These approaches extend the existing estimation procedures and improve the estimation accuracy and convergence rate significantly as proven in our theoretical investigation. Our algorithms are similar to the higher order orthogonal projection method for tensor decomposition, but with significant differences due to the need to unfold tensors in the iterations and the use of autocorrelation. Consequently, our analysis is significantly different from the existing ones. Computational and statistical lower bounds are derived to prove the optimality of the sample size requirement and convergence rate for the proposed methods. Simulation study is conducted to further illustrate the statistical properties of these estimators.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
