In this paper, we address the inference problem in high-dimensional linear expectile regression. We transform the expectile loss into a weighted-least-squares form and apply a de-biased strategy to establish Wald-type tests for multiple constraints within a regularized framework. Simultaneously, we construct an estimator for the pseudo-inverse of the generalized Hessian matrix in high dimension with general amenable regularizers including Lasso and SCAD, and demonstrate its consistency through a new proof technique. We conduct simulation studies and real data applications to demonstrate the efficacy of our proposed test statistic in both homoscedastic and heteroscedastic scenarios.

翻译：本文研究了高维线性期望分位回归中的推断问题。我们将期望分位损失转化为加权最小二乘形式，并采用偏差校正策略，在正则化框架下建立了针对多重约束的Wald型检验。同时，我们针对包含Lasso和SCAD等通用高效正则化器的高维情形，构建了广义海森矩阵伪逆的估计量，并通过一种新的证明技术论证了其相合性。通过模拟实验与真实数据应用，我们证明了所提出的检验统计量在同方差与异方差场景下的有效性。