Edgeworth expansion of a function of sample means

Many important statistics can be written as functions of sample means of vector variables. A fundamental contribution to the Edgeworth expansion for functions of sample means was made by Bhattacharya and Ghosh. In their work the crucial Cramer c-condition is assumed on the joint distribution of all the components of the vector variable. However, in many practical situations, only one or a few of the components satisfy (conditionally) this condition while the rest do not (such a case is referred to as satisfying the partial Cramer c-condition). The purpose of this paper is to establish Edgeworth expansions for functions of sample means when only the partial Cramer c-condition is satisfied