论文标题
强大的甲骨文估计和可能稀疏分位数的不确定性定量
Robust oracle estimation and uncertainty quantification for possibly sparse quantiles
论文作者
论文摘要
一般的许多分位数 +噪声模型以鲁棒公式（允许非正态，非独立的观测值）进行了研究，其中噪声的可识别性要求是根据分位数而不是传统的零期望假设提出的。我们提出了一种基于分位数损失函数的惩罚方法，并通过适当选择的惩罚函数推断可能稀疏的高维分位数矢量。我们通过将程序与甲骨文稀疏结构进行比较来应用本地方法来解决最佳性。我们确定所提出的程序在估计和不确定性定量问题（在所谓的EBR条件下）中模仿了Oracle。自适应minimax的结果超过了稀疏性量表，我们的本地结果遵循。
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.
