Local Regression Distribution Estimators

• Activity Number: 386 - Recent Advances of Causal Inference in Observational Studies
• Type: Invited
• Date/Time: Wednesday, August 5, 2020 : 1:00 PM to 2:50 PM
• Sponsor: WNAR
• Author(s): Xinwei Ma* and Matias Cattaneo and Michael Jansson
• Companies: University of California San Diego and Princeton University and University of California Berkeley
• Keywords: Distribution and density estimation; Local polynomial methods; Uniform approximation; Efficiency; Program evaluation; Causal inference

Abstract

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.