On Bartlett Correction of Empirical Likelihood in the Presence of Nuisance Parameters

Lazar & Mykland (1999) showed that an empirical likelihood defined by two estimating equations with a nuisance parameter need not be Bartlett correctable. This paper shows that Bartlett correction of empirical likelihood in the presence of a nuisance parameter depends critically on the way the nuisance parameter is removed when formulating the likelihood for the parameter of interest. We establish in the broad framework of estimating functions that the empirical likelihood is still Bartlett-correctable if the nuisance parameter is profiled out given the value of the parameter of interest. Some key words: Bartlett correction; Empirical likelihood; Estimation equation; Nuisance parameter.