Smoothed Quantile Regression with Factor-Augmented Regularized Variable Selection for High Correlated Data

Yongxia Zhang, Qi Wang and Maozai Tian ()
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Yongxia Zhang: College of Science, North China University of Technology, Beijing 100144, China
Qi Wang: Key Laboratory of Quantitative Remote Sensing Information Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China
Maozai Tian: School of Statistics, Renmin University of China, Beijing 100872, China

Mathematics, 2022, vol. 10, issue 16, 1-30

Abstract: This paper studies variable selection for the data set, which has heavy-tailed distribution and high correlations within blocks of covariates. Motivated by econometric and financial studies, we consider using quantile regression to model the heavy-tailed distribution data. Considering the case where the covariates are high dimensional and there are high correlations within blocks, we use the latent factor model to reduce the correlations between the covariates and use the conquer to obtain the estimators of quantile regression coefficients, and we propose a consistency strategy named factor-augmented regularized variable selection for quantile regression (Farvsqr). By principal component analysis, we can obtain the latent factors and idiosyncratic components; then, we use both as predictors instead of the covariates with high correlations. Farvsqr transforms the problem from variable selection with highly correlated covariates to that with weakly correlated ones for quantile regression. Variable selection consistency is obtained under mild conditions. Simulation study and real data application demonstrate that our method is better than the common regularized M-estimation LASSO.

Keywords: quantile regression; high correlations; latent factor model; variable selection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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