标题： 高维线性模型中的变量选择，可能具有非对称或重尾误差 显示英文标题

标题： Variable selection in high-dimensional linear model with possibly asymmetric or heavy-tailed errors

摘要： 我们考虑在误差具有不对称或重尾分布的情况下，当解释变量的数量随着样本量的增加而发散时，线性模型中的自动变量选择问题。 对于这个高维模型，惩罚最小二乘方法不适用，而分位数框架使得推断更加困难，因为损失函数的不可微性。 我们提出并研究了一种通过自适应LASSO惩罚期望过程的估计方法。 考虑了两种情况：模型参数的数量小于然后大于样本量，这两种情况通过所考虑的自适应惩罚不同。 对于每种情况，我们给出了收敛速率，并建立了自适应LASSO期望估计量的oracle性质。 所提出的估计量通过蒙特卡洛模拟进行评估，并与自适应LASSO分位数估计量进行比较。 我们还将我们的估计方法应用于遗传学中的真实数据，当参数数量大于样本量时。 显示英文摘要

摘要： 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.