Expansions for von Mises functionals

Summary Berry-Esseen results and expansions are derived for the distribution function of von Mises functionals of order r under moment conditions and conditions on the smoothness of the limit distribution.The results apply to goodness-of-fit statistics — as well as to the central limit theorem in L ^2p,p2, the rate of convergence being O(n ^–1) for centered balls, provided a fourth moment exists.Research sponsored in part under Office of Naval Research. Contract Number N00014-80-C-0163.