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2009 Empty set problem of maximum empirical likelihood methods
Marian Grendár, George Judge
Electron. J. Statist. 3: 1542-1555 (2009). DOI: 10.1214/09-EJS528

Abstract

In an influential work, Qin and Lawless (1994) proposed a general estimating equations (GEE) formulation for maximum empirical likelihood (MEL) estimation and inference. The formulation replaces a model specified by GEE with a set of data-supported probability mass functions that satisfy empirical estimating equations (E3). In this paper we use several examples from the literature to demonstrate that the set may be empty for some E3 models and finite data samples. As a result, MEL does not exist for such models and data sets. If MEL and other E3-based methods are to be used, then models will have to be checked on case-by-case basis for the absence or presence of the empty set problem.

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Marian Grendár. George Judge. "Empty set problem of maximum empirical likelihood methods." Electron. J. Statist. 3 1542 - 1555, 2009. https://doi.org/10.1214/09-EJS528

Information

Published: 2009
First available in Project Euclid: 4 January 2010

zbMATH: 1326.62051
MathSciNet: MR2578837
Digital Object Identifier: 10.1214/09-EJS528

Subjects:
Primary: 62F10

Keywords: affine empty set problem , empirical estimating equations , empirical likelihood , empirical likelihood bootstrap , euclidean empirical likelihood , generalized empirical likelihood , generalized minimum contrast , Model selection

Rights: Copyright © 2009 The Institute of Mathematical Statistics and the Bernoulli Society

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