Open Access
Translator Disclaimer
March, 1990 Pseudo-Likelihood Theory for Empirical Likelihood
Peter Hall
Ann. Statist. 18(1): 121-140 (March, 1990). DOI: 10.1214/aos/1176347495


It is proved that, except for a location term, empirical likelihood does draw contours which are second-order correct for those of a pseudo-likelihood. However, except in the case of one dimension, this pseudo-likelihood is not that which would commonly be employed when constructing a likelihood-based confidence region. It is shown that empirical likelihood regions may be adjusted for location so as to render them second-order correct. Furthermore, it is proved that location-adjusted empirical likelihood regions are Bartlett-correctable, in the sense that a simple empirical scale correction applied to location-adjusted empirical likelihood reduces coverage error by an order of magnitude. However, the location adjustment alters the form of the Bartlett correction. It is also shown that empirical likelihood regions and bootstrap likelihood regions differ to second order, although both are based on statistics whose centered distributions agree to second order.


Download Citation

Peter Hall. "Pseudo-Likelihood Theory for Empirical Likelihood." Ann. Statist. 18 (1) 121 - 140, March, 1990.


Published: March, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0699.62040
MathSciNet: MR1041388
Digital Object Identifier: 10.1214/aos/1176347495

Primary: 62G05
Secondary: 62G10

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.18 • No. 1 • March, 1990
Back to Top