Simple Local Polynomial Density Estimators

TL;DR

This paper proposes a boundary-adaptive local polynomial density estimator that is easy to implement, does not require data transformation, and includes methods for estimation, inference, and bandwidth selection, with applications to discontinuity testing.

Contribution

It introduces a novel, boundary-adaptive local polynomial density estimator along with practical inference and bandwidth selection methods, and applies these to discontinuity testing in regression discontinuity designs.

Findings

Estimator is boundary adaptive and fully automatic.

Provides new methods for density estimation and inference.

Develops a novel discontinuity in density testing procedure.

Abstract

This paper introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not require pre-binning or any other transformation of the data. We study the main asymptotic properties of the estimator, and use these results to provide principled estimation, inference, and bandwidth selection methods. As a substantive application of our results, we develop a novel discontinuity in density testing procedure, an important problem in regression discontinuity designs and other program evaluation settings. An illustrative empirical application is given. Two companion Stata and R software packages are provided.