带约束分位数因子模型中的统计分析方法与应用

大数据技术的发展带来了对高维因子模型大量的应用需求。带约束分位数因子模型不仅能够考察不同分位数水平上的因子波动还能加入对应用背景信息的考量，具有巨大的潜在应用价值。本研究拟针对特质项具有可分相关性假设的带约束分位数因子模型，进行理论与应用层面的研究。拟基于平行分析与赋权主成分分析方法的思想，对同时包含已知约束条件与可识别条件的分位数因子模型提出一套有效、稳健的估计算法，并对所提出的因子结构估计量研究其渐近理论性质。最后，本研究将整合阶段性的研究成果，设计数值模拟实验对所提出的估计量进行分析与评价，并探索带约束分位数因子模型在经济、金融、社会学等领域中的具体应用。

Innovations in big data technology have brought great demands for applications of high dimensional factor model. To account for various structures in co-movements across different quantile levels and possible prior information coming from the background, constrained quantile factor model has been put under the spotlight. This project is intended to work on the development of theories and applications of constrained quantile factor models specifically those with separable idiosyncratic components. Based on the idea originated from parallel analysis and reweighted principle component analysis, an efficient and robust estimation method will be devised for quantile factor models with compound constraints. We will also dig into the studies on theoretical properties of proposed estimator. To formulate all results into papers, we will have estimation method evaluated in numerical simulations and examine model applications in real datasets collected in economics, finance, sociology studies and other related fields.