论文标题
在具有分组变量的高维模型中，通过惩罚的不对称LQ-NORS进行自动选择
Automatic selection by penalized asymmetric Lq-norm in an high-dimensional model with grouped variables
论文作者
论文摘要
当模型误差不对称时，本文着重于高维模型中分组解释变量的自动选择。在介绍了模型和符号之后，我们定义了自适应群体期望估计量，我们证明了Oracle属性：稀疏性和渐近正态性。 之后，通过考虑不对称$ L_Q $ -Norm损失函数来概括结果。在多种情况下，相对于可变组的数量获得了理论结果。该数字可以修复或取决于样本量$ n $，其可能性与$ n $相同。请注意，这些新的估计器使我们能够考虑到数据和模型错误的假设较弱。仿真研究表明，提出的惩罚期望回归的竞争性能，尤其是当样本大小接近解释变量的数量时，模型误差是不对称的。考虑了空气污染数据的应用。
The paper focuses on the automatic selection of the grouped explanatory variables in an high-dimensional model, when the model errors are asymmetric. After introducing the model and notations, we define the adaptive group LASSO expectile estimator for which we prove the oracle properties: the sparsity and the asymptotic normality. Afterwards, the results are generalized by considering the asymmetric $L_q$-norm loss function. The theoretical results are obtained in several cases with respect to the number of variable groups. This number can be fixed or dependent on the sample size $n$, with the possibility that it is of the same order as $n$. Note that these new estimators allow us to consider weaker assumptions on the data and on the model errors than the usual ones. Simulation study demonstrates the competitive performance of the proposed penalized expectile regression, especially when the samples size is close to the number of explanatory variables and model errors are asymmetrical. An application on air pollution data is considered.
