  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.
