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

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