论文标题
高维矩阵变化因子模型的统计推断
Statistical Inference for High-Dimensional Matrix-Variate Factor Model
论文作者
论文摘要
本文考虑了高维矩阵变差因子模型中低级别组件的估计和推断，其中矩阵变量的每个维度（$ p \ times q $）的每个维度与观测值数量相当或大于观测值（$ t $）。我们提出了一种称为$α$ -PCA的估计方法，该方法通过超参数$α$保留了矩阵结构，骨料结构的平均值和现代协方差。在一般条件下，我们开发了一种推论理论，建立一致性，收敛速率和限制分布，从而允许噪声的时间，行或列之间建立相关性。我们显示了选择最佳$α$的理论和经验方法，具体取决于用例标准。仿真结果证明了渐近结果近似有限样品特性的适当性。 $α$ -PCA与现有的$ -PCA比较。最后，我们使用真实的数字数据集和两个真实的图像数据集说明了其应用程序。在所有应用中，提出的估计程序在方差解释的功能方面的先前方法使用样本外10倍交叉验证。
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of observations ($T$). We propose an estimation method called $α$-PCA that preserves the matrix structure and aggregates mean and contemporary covariance through a hyper-parameter $α$. We develop an inferential theory, establishing consistency, the rate of convergence, and the limiting distributions, under general conditions that allow for correlations across time, rows, or columns of the noise. We show both theoretical and empirical methods of choosing the best $α$, depending on the use-case criteria. Simulation results demonstrate the adequacy of the asymptotic results in approximating the finite sample properties. The $α$-PCA compares favorably with the existing ones. Finally, we illustrate its applications with a real numeric data set and two real image data sets. In all applications, the proposed estimation procedure outperforms previous methods in the power of variance explanation using out-of-sample 10-fold cross-validation.
