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March, 1990 Empirical Likelihood Ratio Confidence Regions
Art Owen
Ann. Statist. 18(1): 90-120 (March, 1990). DOI: 10.1214/aos/1176347494

Abstract

An empirical likelihood ratio function is defined and used to obtain confidence regions for vector valued statistical functionals. The result is a nonparametric version of Wilks' theorem and a multivariate generalization of work by Owen. Cornish-Fisher expansions show that the empirical likelihood intervals for a one dimensional mean are less adversely affected by skewness than are those based on Student's $t$ statistic. An effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable. The method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain. Algorithms exist for finding the unique global minimum at a superlinear rate of convergence. A byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points. The multivariate empirical likelihood regions are justified for functions of several means, such as variances, correlations and regression parameters and for statistics with linear estimating equations. An algorithm is given for computing profile empirical likelihoods for these statistics.

Citation

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Art Owen. "Empirical Likelihood Ratio Confidence Regions." Ann. Statist. 18 (1) 90 - 120, March, 1990. https://doi.org/10.1214/aos/1176347494

Information

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

zbMATH: 0712.62040
MathSciNet: MR1041387
Digital Object Identifier: 10.1214/aos/1176347494

Subjects:
Primary: 62E20

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 1 • March, 1990
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