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 random vectors. Our motivation resides on the fact that this could enable subsequent uniform approximations of analogous moments and their derivatives. We derive sufficient conditions either in the case of stochastic processes exhibiting weak dependence, or in the case of smooth transformations of such expansions. The combination of the results can lead to the establishment of high order asymptotic properties for estimators of interest.