A1545
Title: Bridging factor and sparse models
Authors: Marcelo Medeiros - PUC-Rio (Brazil)
Ricardo P Masini - Princeton University (United States)
Ricardo Masini - Princeton University (United States) [presenting]
Abstract: Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimension. They are seemingly mutually exclusive. We propose a simple lifting method that combines the merits of these two models in a supervised learning methodology that allows us to efficiently explore all the information in high-dimensional datasets. The method is based on a flexible model for panel data, called factor-augmented regression model with both observable or latent common factors, as well as idiosyncratic components as high-dimensional covariate variables. This model not only includes both principal component (factor) regression and sparse regression as specific models but also significantly weakens the cross-sectional dependence and hence facilitates model selection and interpretability. The methodology consists of three steps. At each step, the remaining cross-section dependence can be inferred by a novel test for covariance structure in high-dimensions. We developed asymptotic theory for the factor-augmented sparse regression model and demonstrated the validity of the multiplier bootstrap for testing high-dimensional covariance structures. This is further extended to testing high-dimensional partial covariance structures.
