A Uniform-in-$P$ Edgeworth Expansion under Weak Cram\'{e}r Conditions

This paper provides a finite sample bound for the error term in the Edgeworth expansion for a sum of independent, potentially discrete, nonlattice random vectors, using a uniform-in-$P$ version of the weaker Cram'{e}r condition in Angst and Poly (2017). This finite sample bound can be used to derive an Edgeworth expansion that is uniform over the distributions of the random vectors. Using this result, we derive a uniform-in-$P$ higher order expansion of resampling-based distributions.