论文标题
矩阵肯德尔的tau在高维度中：矩阵因子模型的强大统计量
Matrix Kendall's tau in High-dimensions: A Robust Statistic for Matrix Factor Model
论文作者
论文摘要
在本文中，我们首先提出了广义行/列矩阵Kendall's Tau，用于在金融和医学成像等领域无处不在的基质变量观测值。对于矩阵变化的椭圆形轮廓分布后的随机矩阵，我们表明所提出的行/列矩阵肯德尔的特征空间分别与行/柱散点矩阵的特征相吻合，并具有相同的特征值下降顺序。我们对广义行/列矩阵kendall的tau执行特征值分解，以恢复矩阵因子模型的加载空间。我们还建议通过利用行/列矩阵肯德尔tau的特征值比率来估计因子数。从理论上讲，我们在加载空间，因子得分和公共组件中得出估计量的收敛速率，并证明了因子数量的估计器的一致性，而没有任何矩限制在特质上误差。进行了彻底的仿真研究，以表明拟议估计值对现有估计值的鲁棒性更高。分析资产回报的财务数据集和与Covid-19相关的医学成像数据集的分析说明了该方法的经验实用性。
In this article, we first propose generalized row/column matrix Kendall's tau for matrix-variate observations that are ubiquitous in areas such as finance and medical imaging. For a random matrix following a matrix-variate elliptically contoured distribution, we show that the eigenspaces of the proposed row/column matrix Kendall's tau coincide with those of the row/column scatter matrix respectively, with the same descending order of the eigenvalues. We perform eigenvalue decomposition to the generalized row/column matrix Kendall's tau for recovering the loading spaces of the matrix factor model. We also propose to estimate the pair of the factor numbers by exploiting the eigenvalue-ratios of the row/column matrix Kendall's tau. Theoretically, we derive the convergence rates of the estimators for loading spaces, factor scores and common components, and prove the consistency of the estimators for the factor numbers without any moment constraints on the idiosyncratic errors. Thorough simulation studies are conducted to show the higher degree of robustness of the proposed estimators over the existing ones. Analysis of a financial dataset of asset returns and a medical imaging dataset associated with COVID-19 illustrate the empirical usefulness of the proposed method.
