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This article examines the existence of locally uniform Edgeworth expansions for the distributions of parameterized random vectors. This could be useful for the establishment of high-order asymptotic properties for estimators and test statistics that are potentially based on moments of those vectors. We derive sufficient conditions either in the case of stationary stochastic processes exhibiting weak dependence or in the case of smooth transformations of such expansions.

Valid Locally Uniform Edgeworth Expansions for a Class of Weakly Dependent Processes or Sequences of Smooth Transformations