Factor-Adjusted Regularized Model Selection

TL;DR

This paper introduces FarmSelect, a method for high-dimensional sparse regression that effectively handles correlated covariates by separating latent factors, achieving consistent model selection and strong predictive performance.

Contribution

The paper proposes a novel factor-adjusted approach for model selection in high-dimensional regression, improving consistency under correlated covariates.

Findings

Achieves model selection consistency and optimal convergence rates.

Demonstrates strong finite sample performance in simulations.

Flexible method applicable to various high-dimensional problems.

Abstract

This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when the covariates are highly correlated. Motivated by econometric studies, we consider the case where covariate dependence can be reduced through factor model, and propose a consistent strategy named Factor-Adjusted Regularized Model Selection (FarmSelect). By separating the latent factors from idiosyncratic components, we transform the problem from model selection with highly correlated covariates to that with weakly correlated variables. Model selection consistency as well as optimal rates of convergence are obtained under mild conditions. Numerical studies demonstrate the nice finite sample performance in terms of both model selection and out-of-sample prediction. Moreover, our method is flexible in a sense that it pays no price for weakly correlated and uncorrelated cases. Our method is applicable to a wide range of high dimensional sparse regression problems. An R-package FarmSelect is also provided for implementation.