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2019 Improved density and distribution function estimation
Vitaliy Oryshchenko, Richard J. Smith
Electron. J. Statist. 13(2): 3943-3984 (2019). DOI: 10.1214/19-EJS1619


Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due to the systematic use of this extra information. The particular interest here is the estimation of the density or distribution functions of (generalised) residuals in semi-parametric models defined by a finite number of moment restrictions. Such estimates are of great practical interest, being potentially of use for diagnostic purposes, including tests of parametric assumptions on an error distribution, goodness-of-fit tests or tests of overidentifying moment restrictions. The paper gives conditions for the consistency and describes the asymptotic mean squared error properties of the kernel density and distribution estimators proposed in the paper. A simulation study evaluates the small sample performance of these estimators.


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Vitaliy Oryshchenko. Richard J. Smith. "Improved density and distribution function estimation." Electron. J. Statist. 13 (2) 3943 - 3984, 2019.


Received: 1 October 2018; Published: 2019
First available in Project Euclid: 5 October 2019

zbMATH: 07116193
MathSciNet: MR4015785
Digital Object Identifier: 10.1214/19-EJS1619

Primary: 62G07
Secondary: 62G05, 62G20

Keywords: bandwidth , mean squared error , moment conditions , residuals


Vol.13 • No. 2 • 2019
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