高维近似因子模型的适应性估计与推断

本项目将研究高维近似因子模型中的若干假设检验问题以及适应于普遍性的因子个数与协方差矩阵的估计问题。高维近似因子模型在金融、经济等领域中有着广泛的应用，因此针对它的理论研究具有重要的现实意义与需求导向。当前，学术界针对高维近似因子模型的研究主要是在一些较强的假设下——如普遍性假设与误差协方差矩阵稀疏性假设下——对参数进行估计。在该项目中，我们首先对上述两个假设进行统计检验，从而对近似因子模型的适用性提供理论支持并对现存方法的有效性进行判断。进而，我们拟在弱普遍性假设下，提出具有适应性的因子个数与协方差矩阵的估计方法。我们将通过高维随机矩阵理论以及大偏差等方法解决技术瓶颈背后存在的关键科学问题。综上所述，通过在弱条件下对高维近似因子模型的系统分析，该项目将在一定程度上加深人们对因子模型的理解并完善该模型的理论体系。

This project focuses on several hypothesis testing issues and adaptive estimation of the number of factors and covariance matrix in high-dimensional approximate factor model. Due to the wide applications in finance and economics, it is important in practice to analyze the theoretical properties of this model. So far, the existing research works in the literature focus on the estimation problems under certain strong conditions, e.g., the pervasiveness and sparsity conditions. This project first conducts statistical testing for the aforementioned two conditions, in order to check the adaptivity of this model and validity of the existing methods. Furthermore, we aim to develop new adaptive estimation methods for the number of factors and covariance matrix under weak pervasiveness assumption, which enlarges the scope of applications of this model. We will solve the key scientific problems by the large random matrix theory and large deviation results. To sum up, by analyzing high-dimensional approximate factor model under weak conditions, this project will improve our understanding and complement the theoretical framework of the factor model.