标题： 群体稀疏性下的不确定性量化 显示英文标题

标题： Uncertainty Quantification Under Group Sparsity

摘要： 在群体稀疏性下，如群体Lasso，量化惩罚估计量的不确定性是一个重要但仍未解决的问题。 我们在高维尺度下，建立了群体Lasso的估计抽样分布的一致性，假设正态误差模型，并对设计矩阵和真实系数施加了温和的条件。 因此，从估计的抽样分布中进行模拟为构建单个系数和可能的大组系数的区间估计提供了一种有效且方便的方法。 结果进一步推广到其他群体范数惩罚和次高斯误差。 显示英文摘要

摘要： Quantifying the uncertainty in a penalized estimator under group sparsity, such as the group Lasso, is an important, yet still open, question. We establish, under a high-dimensional scaling, the consistency of an estimated sampling distribution for the group Lasso, assuming a normal error model and mild conditions on the design matrix and the true coefficients. Consequently, simulation from the estimated sampling distribution provides a valid and convenient means of constructing interval estimates for both individual coefficients and potentially large groups of coefficients. The results are further generalized to other group norm penalties and sub-Gaussian errors.