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.

中文翻译：

---

可能存在非对称误差的高维线性模型中的变量选择

在许多应用领域，当解释变量的数量随着样本量的变化而发散时，会遇到具有非对称误差的线性模型中自动选择变量的问题。对于这种高维模型，惩罚最小二乘法是不合适的，分位数框架由于损失函数的不可微性使得推理更加困难。提出并研究了一种用自适应LASSO惩罚惩罚期望过程的估计方法。考虑两种情况：首先假设模型参数的数量远小于样本量，然后可能是相同的数量级；这两种情况因考虑的适应性惩罚而不同。对于每种情况，获得了速率收敛并建立了自适应LASSO期望估计器的预言性质。建议的估计器通过蒙特卡罗模拟进行评估，并与自适应 LASSO 分位数估计器进行比较。所提出的估计方法也适用于遗传学中的真实数据。