Onm-dependence and Edgeworth expansions

This paper contains two results. The first establishes, under mild assumptions, the validity of an Edgeworth expansion with remaindero(N ^–1/2) for aU-statistic with a kernel of degree two using observations from anm-dependent shift. The second result gives a necessary and sufficient condition for the distribution of a sum ofm-dependent random variables to possess an Edgeworth expansion. This generalizes a result of Bickel and Robinson from the i.i.d. case to them-dependent case.This research was supported in part by National Science Foundation, Grant DMS 89-23071.