Approximate jackknife empirical likelihood method for estimating equations

It is known that the profile empirical likelihood method based on estimating equations is computationally intensive when the number of nuisance parameters is large. Recently, Li, Peng, & Qi (2011) proposed a jackknife empirical likelihood method for constructing confidence regions for the parameters of interest by estimating the nuisance parameters separately. However, when the estimators for the nuisance parameters have no explicit formula, the computation of the jackknife empirical likelihood method is still intensive. In this paper, an approximate jackknife empirical likelihood method is proposed to reduce the computation in the jackknife empirical likelihood method when the nuisance parameters cannot be estimated explicitly. A simulation study confirms the advantage of the new method. The Canadian Journal of Statistics 40: 110–123; 2012 © 2012 Statistical Society of Canada