Electronic Journal of Statistics

A note on residual-based empirical likelihood kernel density estimation

Birte Muhsal and Natalie Neumeyer

Full-text: Open access

Abstract

In general the empirical likelihood method can improve the performance of estimators by including additional information about the underlying data distribution. Application of the method to kernel density estimation based on independent and identically distributed data always improves the estimation in second order. In this paper we consider estimation of the error density in nonparametric regression by residual-based kernel estimation. We investigate whether the estimator is improved when additional information is included by the empirical likelihood method. We show that the convergence rate is not effected, but in comparison to the residual-based kernel estimator we observe a change in the asymptotic bias of the empirical likelihood estimator in first order and in the asymptotic variance in second order. Those changes do not result in a general uniform improvement of the estimation, but in typical examples we demonstrate the good performance of the residual-based empirical likelihood estimator in asymptotic theory as well as in simulations.

Article information

Source
Electron. J. Statist., Volume 4 (2010), 1386-1401.

Dates
First available in Project Euclid: 9 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1291903542

Digital Object Identifier
doi:10.1214/10-EJS586

Mathematical Reviews number (MathSciNet)
MR2741205

Zentralblatt MATH identifier
1329.62190

Subjects
Primary: 62G07: Density estimation
Secondary: 62G08: Nonparametric regression

Keywords
Asymptotic mean squared error error distribution kernel estimation likelihood method nonparametric regression second order expansions

Citation

Muhsal, Birte; Neumeyer, Natalie. A note on residual-based empirical likelihood kernel density estimation. Electron. J. Statist. 4 (2010), 1386--1401. doi:10.1214/10-EJS586. https://projecteuclid.org/euclid.ejs/1291903542


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