Empty Set Problem of Maximum Empirical Likelihood Methods

Electronic Journal of Statistics, Vol. 3, pp. 1542-1555, 2009

14 Pages Posted: 19 Jan 2010

See all articles by Marian Grendar

Marian Grendar

Bel University; Institute of Measurement Science, Slovak Academy of Sciences; Institute of Mathematics and CS, Bel Univesity & SAS

George Judge

University of California, Berkeley - Department of Agricultural & Resource Economics

Date Written: January 19, 2010

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.

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

Suggested Citation

Grendar, Marian and Judge, George G., Empty Set Problem of Maximum Empirical Likelihood Methods (January 19, 2010). Electronic Journal of Statistics, Vol. 3, pp. 1542-1555, 2009 , Available at SSRN: https://ssrn.com/abstract=1539129 or http://dx.doi.org/10.2139/ssrn.1539129

Marian Grendar (Contact Author)

Bel University ( email )

Tajovskeho 40
SK-974 01 Banska Bystrica
Slovakia

Institute of Measurement Science, Slovak Academy of Sciences ( email )

Tajovskeho 40
SK-974 01 Banska Bystrica
Slovakia

Institute of Mathematics and CS, Bel Univesity & SAS ( email )

Tajovskeho 40
SK-974 01 Banska Bystrica
Slovakia

George G. Judge

University of California, Berkeley - Department of Agricultural & Resource Economics ( email )

207 Giannini Hall
University of California
Berkeley, CA 94720
United States

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