桥接因子和稀疏模型
Bridging factor and sparse models
摘要：
因子模型和稀疏模型是两种广泛使用的在高维中施加低维结构的方法。然而，它们似乎是相互排斥的。我们提出了一种提升方法，它结合了这两种模型在监督学习方法中的优点，可以有效地探索高维数据集中的所有信息。该方法是基于一个灵活的模型，高维面板数据，称为因子增广回归模型与可观察的和/或潜在的共同因素，以及特质成分。该模型不仅包括主成分回归和稀疏回归作为具体的模型，但也显着削弱了横截面的依赖性，有利于模型的选择和解释。该方法包括几个步骤和一个新的测试（部分）协方差结构在高维推断剩余的横截面依赖在每一步。我们开发的理论模型，并证明了有效性的乘数自助测试高维（部分）协方差结构。该理论得到了仿真研究和应用的支持。
英文摘要：
Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimensions. However, they are seemingly mutually exclusive. We propose a lifting method that combines the merits of these two models in a supervised learning methodology that allows for efficiently exploring all the information in high-dimensional datasets. The method is based on a flexible model for high-dimensional panel data, called factor-augmented regression model with observable and/or latent common factors, as well as idiosyncratic components. This model not only includes both principal component regression and sparse regression as specific models but also significantly weakens the cross-sectional dependence and facilitates model selection and interpretability. The method consists of several steps and a novel test for (partial) covariance structure in high dimensions to infer the remaining cross-section dependence at each step. We develop the theory for the model and demonstrate the validity of the multiplier bootstrap for testing a high-dimensional (partial) covariance structure. The theory is supported by a simulation study and applications.
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