Empty set problem of maximum empirical likelihood methods

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.