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August 2013 Empirical likelihood on the full parameter space
Min Tsao, Fan Wu
Ann. Statist. 41(4): 2176-2196 (August 2013). DOI: 10.1214/13-AOS1143

Abstract

We extend the empirical likelihood of Owen [Ann. Statist. 18 (1990) 90–120] by partitioning its domain into the collection of its contours and mapping the contours through a continuous sequence of similarity transformations onto the full parameter space. The resulting extended empirical likelihood is a natural generalization of the original empirical likelihood to the full parameter space; it has the same asymptotic properties and identically shaped contours as the original empirical likelihood. It can also attain the second order accuracy of the Bartlett corrected empirical likelihood of DiCiccio, Hall and Romano [Ann. Statist. 19 (1991) 1053–1061]. A simple first order extended empirical likelihood is found to be substantially more accurate than the original empirical likelihood. It is also more accurate than available second order empirical likelihood methods in most small sample situations and competitive in accuracy in large sample situations. Importantly, in many one-dimensional applications this first order extended empirical likelihood is accurate for sample sizes as small as ten, making it a practical and reliable choice for small sample empirical likelihood inference.

Citation

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Min Tsao. Fan Wu. "Empirical likelihood on the full parameter space." Ann. Statist. 41 (4) 2176 - 2196, August 2013. https://doi.org/10.1214/13-AOS1143

Information

Published: August 2013
First available in Project Euclid: 23 October 2013

zbMATH: 1360.62140
MathSciNet: MR3127862
Digital Object Identifier: 10.1214/13-AOS1143

Subjects:
Primary: 62G20
Secondary: 62E20

Keywords: Bartlett correction , composite similarity transformation , empirical likelihood , extended empirical likelihood , similarity transformation

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 4 • August 2013
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