Valid Locally Uniform Edgeworth Expansions Under Weak Dependence and Sequences of Smooth Transformations

In this paper we are concerned with the issue of the existence of locally uniform Edgeworth expansions for the distributions of parameterized random vectors. Our motivation resides on the fact that this could enable subsequent polynomial asymptotic expansions of moments. These could be useful for the establishment of asymptotic properties for estimators based on these moments. We derive sufficient conditions either in the case of stochastic processes exhibiting weak dependence, or in the case of smooth transformations of such expansions.