Confidence sets in sparse regression
研究了高维线性模型中构建置信集的问题，给出了稀疏自适应置信集存在的充要条件，适用于参数空间的最小ℓ²分离条件，涵盖次高斯设计。
The problem of constructing confidence sets in the high-dimensional linear model with $n$ response variables and $p$ parameters, possibly $p\ge n$, is considered. Full honest adaptive inference is possible if the rate of sparse estimation does not exceed $n^{-1/4}$, otherwise sparse adaptive confidence sets exist only over strict subsets of the parameter spaces for which sparse estimators exist. Necessary and sufficient conditions for the existence of confidence sets that adapt to a fixed sparsity level of the parameter vector are given in terms of minimal $\ell^{2}$-separation conditions on the parameter space. The design conditions cover common coherence assumptions used in models for sparsity, including (possibly correlated) sub-Gaussian designs.