Comparison of tests in the multiparameter case II. A third-order optimality property of Rao's test

AbstractIn a general multiparameter setup, this paper proves an optimality property of Rao's test, in terms of maximization of “average” third-order power under contiguous alternatives, within a very wide class of tests that includes the likelihood ratio and Wald's tests. The use of a new kind of polynomials, analogous to Hermite polynomials, is helpful in the derivation of the results