BRIDGING FACTOR AND SPARSE MODELS

doi:10.1214/23-AOS2304

BRIDGING FACTOR AND SPARSE MODELS

2023-08-01

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DOI：10.1214/23-AOS2304

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Factor and sparse models are widely used 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 with observable and/or latent common factors and idiosyncratic components. The model is called the factor-augmented regression model. It includes principal components and sparse regression as specific models, significantly weakens the crosssectional 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. A simulation study and applications support the theory.

Keywords:

Factor models

penalized least-squares

high-dimensional inference

(partial) covari-ance structure

prediction

machine learning

supervised learning

BRIDGING FACTOR AND SPARSE MODELS

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