Shrinkage for categorical regressors
Shrinkage for categorical regressors
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DOI：
10.1016/j.jeconom.2020.07.051
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发表时间：
2019-01
影响因子：
6.3
通讯作者：
Phillip Heiler;J. Marecková
中科院分区：
文献类型：
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作者：
Phillip Heiler;J. Marecková
本文介绍了一种灵活的正则化方法，减少了点估计的风险，组的意思是来自分类回归，（准）实验数据或面板数据模型。损失函数通过添加组位置参数和信息第一阶段估计之间的加权平方2范数差来惩罚。在二次损失下，惩罚估计问题有一个简单的可解释的封闭形式的解决方案，嵌套方法建立在文献中的岭回归，离散支持平滑内核和模型平均方法。我们推导出风险最优的惩罚参数，并提出了一个插件的估计方法。大样本的性质进行了分析，在一个渐进的本地到零的框架，通过引入一类序列的位置，足以描述大范围的数据生成过程的密切和遥远的系统。在不同的惩罚方案下，我们给出了收缩估计的渐近分布。建议的插件估计一致优于普通的最小二乘估计的渐近风险，如果组的数量大于3。Monte Carlo模拟显示，在有限样本的标准方法的强大的改进。真实的数据的例子估计的时间趋势的面板和差异中的差异研究说明了潜在的应用。
This paper introduces a flexible regularization approach that reduces point estimation risk of group means stemming from eg categorical regressors,(quasi-) experimental data or panel data models. The loss function is penalized by adding weighted squared ℓ 2-norm differences between group location parameters and informative first stage estimates. Under quadratic loss, the penalized estimation problem has a simple interpretable closed-form solution that nests methods established in the literature on ridge regression, discretized support smoothing kernels and model averaging methods. We derive risk-optimal penalty parameters and propose a plug-in approach for estimation. The large sample properties are analyzed in an asymptotic local to zero framework by introducing a class of sequences for close and distant systems of locations that is sufficient for describing a large range of data generating processes. We provide the asymptotic distributions of the shrinkage estimators under different penalization schemes. The proposed plug-in estimator uniformly dominates the ordinary least squares estimator in terms of asymptotic risk if the number of groups is larger than three. Monte Carlo simulations reveal robust improvements over standard methods in finite samples. Real data examples of estimating time trends in a panel and a difference-in-differences study illustrate potential applications.