This paper studies the asymptotic properties of a sparse linear regression estimator, referred to as broken adaptive ridge (BAR) estimator, resulting from an L 0-based iteratively reweighted L 2 penalization algorithm using the ridge estimator as its initial value. We show that the BAR estimator is consistent for variable selection and has an oracle property for parameter estimation. Moreover, we show that the BAR estimator possesses a grouping effect: highly correlated covariates are naturally grouped together, which is a desirable property not known for other oracle variable selection methods. Lastly, we combine BAR with a sparsity-restricted least squares estimator and give conditions under which the resulting two-stage sparse regression method is selection and estimation consistent in addition to having the grouping property in high- or ultrahigh-dimensional settings. Numerical studies are conducted to investigate and illustrate the operating characteristics of the BAR method in comparison with other methods.

中文翻译：

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破碎自适应岭回归及其渐近性质


本文研究了稀疏线性回归估计器（称为破碎自适应岭（BAR）估计器）的渐近特性，该估计器由使用岭估计器作为初始值的基于 L 0 的迭代重加权 L 2 惩罚算法产生。我们证明了 BAR 估计器对于变量选择是一致的，并且对于参数估计具有预言性。此外，我们表明 BAR 估计器具有分组效应：高度相关的协变量自然地分组在一起，这是其他预言机变量选择方法所不具备的理想特性。最后，我们将 BAR 与稀疏限制最小二乘估计器相结合，并给出了所得到的两阶段稀疏回归方法除了在高维或超高维设置中具有分组属性之外，选择和估计一致的条件。进行数值研究是为了调查和说明 BAR 方法与其他方法相比的操作特性。