A general many quantiles + noise model is studied in the robust formulation (allowing non-normal, non-independent observations), where the identifiability requirement for the noise is formulated in terms of quantiles rather than the traditional zero expectation assumption. We propose a penalization method based on the quantile loss function with appropriately chosen penalty function making inference on possibly sparse high-dimensional quantile vector. We apply a local approach to address the optimality by comparing procedures to the oracle sparsity structure. We establish that the proposed procedure mimics the oracle in the problems of estimation and uncertainty quantification (under the so called EBR condition). Adaptive minimax results over sparsity scale follow from our local results.

翻译：在稳健的配方(允许非正常、非独立观测)中,对噪音的可识别性要求是用四分位数而不是传统的零预期假设来拟订的,我们提议基于四分位数损失函数的惩罚方法,并适当选择惩罚功能,对可能稀疏的高维四分位矢量进行推断。我们采用当地办法,通过比较程序与触角孔径结构来处理最佳性。我们确定,拟议的程序模仿估计和不确定性量化问题(在所谓的“ERBR条件”下)的奥骨骨。适应性微缩结果大于宽度尺度,取自我们的本地结果。