Abstract:
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This paper investigates 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 a uniform linearization and a strong approximation for the estimators, and employ these results to construct valid confidence bands and two-sample testing procedures. Third, we develop extensions to weighted distributions with estimated weights, and to more general estimation using a local L2 projection. 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 Stata and R are provided.
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