In full rank multivariate exponential families of lattice distributions, one sided testing problems are considered. For these testing problems the uniformly most powerful unbiased tests are not uniformly efficient of order o(n-1) in the class 2* of all tests which are asymptotically similar of...

As is well known, in full rank multivariate exponential families, tests of Neyman structure are uniformly most powerful unbiased for one-sided problems. For the case of lattice distributions, the power of these tests--evaluated at contiguous alternatives--is approximated by asymptotic expansions...