Factor-adjusted regularized model selection

Jianqing Fan Yuan Ke Kaizheng Wang

Statistics Theory and Methods mathscidoc:1912.43405

Available at SSRN 3248047, 2020.9
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.
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  title={Factor-adjusted regularized model selection},
  author={Jianqing Fan, Yuan Ke, and Kaizheng Wang},
  booktitle={Available at SSRN 3248047},
Jianqing Fan, Yuan Ke, and Kaizheng Wang. Factor-adjusted regularized model selection. 2020. In Available at SSRN 3248047. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114230048597965.
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