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摘要翻译：
本文介绍了一种灵活的正则化方法，该方法降低了由类别回归、（准）实验数据或面板数据模型引起的群均值点估计风险。损失函数是通过增加组位置参数和信息第一阶段估计之间的加权平方L2范数差来惩罚的。在二次损失下，惩罚估计问题有一个简单的可解释的封闭解，它嵌套了文献中建立的岭回归、离散支持平滑核和模型平均方法。我们导出了风险最优惩罚参数，并提出了一种用于估计的插件方法。在一个渐近局部零的框架下，通过引入一类足够描述大范围数据生成过程的近距离和远距离位置系统序列，分析了大样本性质。给出了不同惩罚方案下收缩估计的渐近分布。当组数大于3时，所提出的插件估计在渐近风险方面一致支配普通最小二乘估计。Monte Carlo模拟表明，在有限样本中，与标准方法相比，该方法有很好的改进。在面板中估计时间趋势的真实数据例子和差异中的差异研究说明了潜在的应用。
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英文标题：
《Shrinkage for Categorical Regressors》
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作者：
Phillip Heiler, Jana Mareckova
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最新提交年份：
2019
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分类信息：
一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
This paper introduces a flexible regularization approach that reduces point estimation risk of group means stemming from e.g. categorical regressors, (quasi-)experimental data or panel data models. The loss function is penalized by adding weighted squared l2-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 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.
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PDF链接：
https://arxiv.org/pdf/1901.01898
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