中文摘要
变量相关性对大数据建模中的各类 LASSO 型收缩方法构成重大挑战。本文提出了一个相关稳健收缩估计量的完整框架，在高维估计的理论与实践两方面均有所推进。我们将惩罚项分解为“收缩”项与“分组”项，阐明其在聚类高度相关变量方面的独特性质。我们在关于混合条件和较重尾分布的放宽假设下，建立了该估计量的（非）渐近性质。此外，我们证明了模型选择在温和条件下的相合性。我们还提出了该估计量的去偏版本，并证明了其渐近正态性。模拟数据表明，去偏估计量优于传统基准方法。在一项实证应用中，我们使用该去偏估计量识别出解释通胀水平的关键经济政策不确定性（EPU）因子。我们的发现意味着，基于新闻的 EPU 因子在解释 CPI 动态方面至关重要。
Abstract
Variable correlations pose significant challenges for various LASSO-type shrinkage methods in big-data modeling. This paper presents a comprehensive framework for a correlation-robust shrinkage estimator, enhancing both the theoretical and practical aspects of high-dimensional estimation. We break down the penalty term into a “shrinkage” term and a “grouping” term, illustrating its distinctive properties in clustering highly correlated variables. We establish the (non-)asymptotic properties of this estimator under relaxed assumptions regarding mixing conditions and heavier-tailed distributions. Furthermore, we demonstrate the consistency of model selection under mild conditions. Additionally, we propose a debiased version of the estimator, proving its asymptotic normality. Simulated data indicate that the debiased estimator surpasses traditional benchmarks. In an empirical application, we use this debiased estimator to identify key Economic Policy Uncertainty (EPU) factors that account for inflation levels. Our findings imply that news-based EPU factors are essential in explaining CPI dynamics.