The Annals of Statistics

Pseudo-Likelihood Theory for Empirical Likelihood

Peter Hall

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 18, Number 1 (1990), 121-140.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347495

Digital Object Identifier
doi:10.1214/aos/1176347495

Mathematical Reviews number (MathSciNet)
MR1041388

Zentralblatt MATH identifier
0699.62040

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G10: Hypothesis testing

Keywords
Bootstrap likelihood confidence interval Cornish-Fisher expansion coverage Edgeworth expansion empirical likelihood pseudo-likelihood second-order correct

Citation

Hall, Peter. Pseudo-Likelihood Theory for Empirical Likelihood. Ann. Statist. 18 (1990), no. 1, 121--140. doi:10.1214/aos/1176347495. https://projecteuclid.org/euclid.aos/1176347495


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