  We consider the problem of automatic variable selection in a linear model
with asymmetric or heavy-tailed errors when the number of explanatory variables
diverges with the sample size. For this high-dimensional model, the penalized
least square method is not appropriate and the quantile framework makes the
inference more difficult because to the non differentiability of the loss
function. We propose and study an estimation method by penalizing the expectile
process with an adaptive LASSO penalty. Two cases are considered: the number of
model parameters is smaller and afterwards larger than the sample size, the two
cases being distinct by the adaptive penalties considered. For each case we
give the rate convergence and establish the oracle properties of the adaptive
LASSO expectile estimator. The proposed estimators are evaluated through Monte
Carlo simulations and compared with the adaptive LASSO quantile estimator. We
applied also our estimation method to real data in genetics when the number of
parameters is greater than the sample size.
