Baggerly (1998) showed that empirical likelihood is the only member in the Cressie-Read power divergence family to be Bartlett correctable. This paper strengthens Baggerly’s result by showing that in a generalized class of the power divergence family, which includes the Cressie-Read family and other nonparametric likelihood such as Schennach’s (2005, 2007) exponentially tilted empirical likelihood, empirical likelihood is still the only member to be Bartlett correctable.
Camponovo, Lorenzo and Otsu, Taisuke, "On Bartlett Correctability of Empirical Likelihood in Generalized Power Divergence Family" (2011). Cowles Foundation Discussion Papers. 2178.