Computing empirical likelihood from the bootstrap

The close relationship between the bootstrap and empirical likelihood has been noted in the literature. The purpose of this paper is to show how to construct a bootstrap likelihood from a single bootstrap, without any nested bootstrapping nor any smoothing. For a wide class of M-estimators the likelihood agrees with the empirical likelihood up to order O(n-1/2). The resulting likelihood may be used for display purpose, for computing likelihood-based confidence intervals or for future use in combining information.