Nonparametric estimation and testing on discontinuity of positive supported densities: a kernel truncation approach

Benedikt Funke and Masayuki Hirukawa

Econometrics and Statistics, 2019, vol. 9, issue C, 156-170

Abstract: Discontinuity in density functions is of economic importance and interest. For instance, in studies on regression discontinuity designs, discontinuity in the density of a running variable suggests violation of the no-manipulation assumption. In line with this notion, estimation and testing procedures on discontinuity in densities with positive support are developed. The proposed approach is built on splitting the asymmetric, gamma kernel into two parts at a prespecified cutoff that is suspected to be a discontinuity point and constructing two truncated kernels. The jump-size magnitude of the density at the cutoff can be estimated nonparametrically by two kernels and a multiplicative bias correction method. The estimator is easy to implement, and its convergence properties are delivered by various approximation techniques on incomplete gamma functions. Based on the jump-size estimator, two versions of test statistics for the null of continuity at a given cutoff are also proposed. Moreover, estimation theory of the entire density in the presence of a discontinuity point is explored. Monte Carlo simulations confirm nice finite-sample properties of the jump-size estimator and the test statistics.

Keywords: Density estimation; Discontinuous probability density; Gamma kernel; Incomplete gamma functions; Nonparametric kernel testing; Regression discontinuity design (search for similar items in EconPapers)
JEL-codes: C12 C13 C14 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S2452306217300679
Full text for ScienceDirect subscribers only. Contains open access articles

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ecosta:v:9:y:2019:i:c:p:156-170

DOI: 10.1016/j.ecosta.2017.07.006

Access Statistics for this article

Econometrics and Statistics is currently edited by E.J. Kontoghiorghes, H. Van Dijk and A.M. Colubi

More articles in Econometrics and Statistics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().