Second-order power comparisons for a class of nonparametric likelihood-based tests

This paper compares the second-order power properties of a broad class of nonparametric likelihood tests recently introduced by Baggerly (1998) as a generalisation of Owen's (1988) empirical likelihood.It is shown that in a multi-parameter setting identity of power up to first order does not imply identity up to second order unless one considers the average power criterion. It is also shown that the empirical likelihood ratio enjoys an optimality property in terms of local maximinity.