Factor-Adjusted Regularized Model Selection

39 Pages Posted: 3 Oct 2018

See all articles by Jianqing Fan

Jianqing Fan

Princeton University - Bendheim Center for Finance

Yuan Ke

Princeton University - Department of Operations Research & Financial Engineering (ORFE)

Kaizheng Wang

Princeton University - Department of Operations Research & Financial Engineering (ORFE)

Date Written: September 11, 2018

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.

Keywords: High dimension, Model selection consistency, Correlated covariates, Factor model, Regularized M-estimator, Time series

JEL Classification: C38, C52, C58

Suggested Citation

Fan, Jianqing and Ke, Yuan and Wang, Kaizheng, Factor-Adjusted Regularized Model Selection (September 11, 2018). Available at SSRN: https://ssrn.com/abstract=3248047 or http://dx.doi.org/10.2139/ssrn.3248047

Jianqing Fan

Princeton University - Bendheim Center for Finance ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States
609-258-7924 (Phone)
609-258-8551 (Fax)

HOME PAGE: http://orfe.princeton.edu/~jqfan/

Yuan Ke

Princeton University - Department of Operations Research & Financial Engineering (ORFE) ( email )

Sherrerd Hall, Charlton Street
Princeton, NJ 08544
United States

Kaizheng Wang (Contact Author)

Princeton University - Department of Operations Research & Financial Engineering (ORFE) ( email )

Sherrerd Hall, Charlton Street
Princeton, NJ 08544
United States

Register to save articles to
your library

Register

Paper statistics

Downloads
25
Abstract Views
132
PlumX Metrics
!

Under construction: SSRN citations will be offline until July when we will launch a brand new and improved citations service, check here for more details.

For more information