This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample distributional approximation in a unified way, allowing for both boundary and interior evaluation points simultaneously. Using this result, we study the asymptotic efficiency of the estimators, and show that a carefully crafted minimum distance implementation based on “redundant” regressors can lead to efficiency gains. Second, we establish uniform linearizations and strong approximations for the estimators, and employ these results to construct valid confidence bands. Third, we develop extensions to weighted distributions with estimated weights and to local estimation. Finally, we illustrate our methods with two applications in program evaluation: counterfactual density testing, and IV specification and heterogeneity density analysis. Companion software packages in and are available.

中文翻译：

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局部回归分布估计器

本文研究了局部回归分布估计器的大样本特性，其中包括一类边界自适应密度估计器作为主要示例。首先，我们以统一的方式建立点状高斯大样本分布近似，同时允许边界和内部评估点。利用这一结果，我们研究了估计器的渐近效率，并表明基于“冗余”回归器精心设计的最小距离实现可以带来效率增益。其次，我们为估计量建立统一的线性化和强近似，并利用这些结果来构建有效的置信带。第三，我们开发了带有估计权重的加权分布和局部估计的扩展。最后，我们通过程序评估中的两个应用来说明我们的方法：反事实密度测试以及 IV 规范和异质性密度分析。和 中的配套软件包可用。