Variable selection in high-dimensional linear model with possibly asymmetric errors

Abstract

In many application areas, the problem of the automatic variable selection in a linear model with asymmetric errors is encountered, when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least squares method is not appropriate and the quantile framework makes the inference more difficult because of the non differentiability of the loss function. An estimation method by penalizing the expectile process with an adaptive LASSO penalty is proposed and studied. Two cases are considered: first with the number of model parameters is assumed to be much smaller than the sample size and afterwards it could be of the same order; the two cases being distinct by the adaptive penalties considered. For each case, the rate convergence is obtained and the oracle properties of the adaptive LASSO expectile estimator are established. The proposed estimators are evaluated through Monte Carlo simulations and compared with the adaptive LASSO quantile estimator. The proposed estimation method is also applied to real data in genetics.