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

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.