Let P[eta], [eta] = ([theta], [gamma]) [set membership, variant] [Theta] - [Gamma] [subset of] - k, be a (k + 1)-dimensional exponential family. Let [phi]n*, n [set membership, variant] , be an optimal similar test for the hypothesis {P([theta],[gamma])n: [gamma] [set membership, variant]...

It is shown that the probability that a suitably standardized asymptotic maximum likelihood estimator of a vector parameter (i.e., an estimator which approximates the solution of the likelihood equation in a reasonably good way) lies in a measurable convex set can be approximated by an integral...