TY - JOUR
T1 - Factor-adjusted regularized model selection
AU - Fan, Jianqing
AU - Ke, Yuan
AU - Wang, Kaizheng
N1 - Funding Information:
This research was supported in part by the National Science Foundation (NSF), USA grants DMS-1662139 and DMS-1712591 , by the Office of Naval Research (ONR), USA grant N00014-19-1-2120 , and by the National Institutes of Health (NIH), USA grant 2R01-GM072611-13 .
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/5
Y1 - 2020/5
N2 - 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 and financial studies, we consider the case where covariate dependence can be reduced through the factor model, and propose a consistency strategy named Factor-Adjusted Regularized Model Selection (FarmSelect). By learning the latent factors and idiosyncratic components and using both of them as predictors, FarmSelect transforms the problem from model selection with highly correlated covariates to that with weakly correlated ones via lifting. 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 the 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.
AB - 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 and financial studies, we consider the case where covariate dependence can be reduced through the factor model, and propose a consistency strategy named Factor-Adjusted Regularized Model Selection (FarmSelect). By learning the latent factors and idiosyncratic components and using both of them as predictors, FarmSelect transforms the problem from model selection with highly correlated covariates to that with weakly correlated ones via lifting. 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 the 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.
KW - Correlated covariates
KW - Factor model
KW - Model selection consistency
KW - Regularized M-estimator
KW - Time series
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U2 - 10.1016/j.jeconom.2020.01.006
DO - 10.1016/j.jeconom.2020.01.006
M3 - Article
C2 - 32269406
AN - SCOPUS:85079056505
SN - 0304-4076
VL - 216
SP - 71
EP - 85
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 1
ER -