Abstract Many large-scale applications of regression models have correlated data. Although a variety of methods have been developed for this modeling problem, yet it is still challenging to keep an accurate estimation. We propose an adaptive and “reversed” penalty, which focuses on removing the shrinking bias and encouraging the grouping effect. Combining the L 1 penalty and the Minimax Concave Penalty, we propose two methods called Smooth Adjustment for Correlated Effects and Generalized Smooth Adjustment for Correlated Effects. They can be seen as special adaptive estimators, but different from the traditional adaptive estimators that highly rely on the initial estimation. The proposed estimators obtain valid information even from the wrong initial estimates, providing stable and accurate estimation from finite samples. Under mild regularity conditions, we prove that the methods satisfy oracle property. Simulations show that the proposed procedures estimate the coefficients accurately in correlation structures. We also apply the proposed estimator to financial data and show that it is successful in asset allocation selection.

中文翻译：

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高维相关数据分析的自适应和反向惩罚

摘要 回归模型的许多大规模应用都有相关数据。尽管已经针对该建模问题开发了多种方法，但保持准确估计仍然具有挑战性。我们提出了一种自适应和“反向”惩罚，其重点是消除收缩偏差并鼓励分组效应。结合L 1 惩罚和Minimax Concave Penalty，我们提出了两种方法，称为相关效应的平滑调整和相关效应的广义平滑调整。它们可以看作是特殊的自适应估计器，但不同于高度依赖初始估计的传统自适应估计器。即使从错误的初始估计中，建议的估计器也能获得有效信息，从有限样本中提供稳定和准确的估计。在温和的正则性条件下，我们证明了这些方法满足预言机性质。模拟表明，所提出的程序可以准确地估计相关结构中的系数。我们还将建议的估计量应用于财务数据，并表明它在资产配置选择方面是成功的。