Bridging factor and sparse models

2023/08/01 by Jianqing Fan, Ricardo P. Masini, Ricardo Masini +1
Economics, Econometrics and Finance · Mathematics · #Spatial and Panel Data Analysis #Statistical Methods and Inference #Housing Market and Economics

paper · doi:10.1214/23-aos2304

Abstract

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 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. A simulation study and applications support the theory.

Citations

• The Generalized Dynamic-Factor Model: Identification and Estimation
• A well-conditioned estimator for large-dimensional covariance matrices
• Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure

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