Transformations of multivariate Edgeworth type expansions

Given a random vector whose distribution can be expanded in powers of some parameter εε (such as the Edgeworth expansion with ε=n−1/2ε=n−1/2 and nn the sample size), methods are given for expanding the distribution of a transformation of it in powers of εε. Under specified conditions the derived expansion reduces to one in powers of ε2ε2. Applications are made to lattice and non-lattice random variables and to stationary series.