Open Access
June 2010 Adjusted empirical likelihood with high-order precision
Yukun Liu, Jiahua Chen
Ann. Statist. 38(3): 1341-1362 (June 2010). DOI: 10.1214/09-AOS750


Empirical likelihood is a popular nonparametric or semi-parametric statistical method with many nice statistical properties. Yet when the sample size is small, or the dimension of the accompanying estimating function is high, the application of the empirical likelihood method can be hindered by low precision of the chi-square approximation and by nonexistence of solutions to the estimating equations. In this paper, we show that the adjusted empirical likelihood is effective at addressing both problems. With a specific level of adjustment, the adjusted empirical likelihood achieves the high-order precision of the Bartlett correction, in addition to the advantage of a guaranteed solution to the estimating equations. Simulation results indicate that the confidence regions constructed by the adjusted empirical likelihood have coverage probabilities comparable to or substantially more accurate than the original empirical likelihood enhanced by the Bartlett correction.


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Yukun Liu. Jiahua Chen. "Adjusted empirical likelihood with high-order precision." Ann. Statist. 38 (3) 1341 - 1362, June 2010.


Published: June 2010
First available in Project Euclid: 8 March 2010

zbMATH: 1189.62054
MathSciNet: MR2662345
Digital Object Identifier: 10.1214/09-AOS750

Primary: 62G20
Secondary: 62E20

Keywords: Bartlett correction , confidence region , Edgeworth expansion , estimating function , generalized moment method

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 3 • June 2010
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