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,p≧2, the rate of convergence being O(n −1) for centered balls, provided a fourth moment exists.
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Research sponsored in part under Office of Naval Research. Contract Number N00014-80-C-0163.
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Götze, F. Expansions for von Mises functionals. Z. Wahrscheinlichkeitstheorie verw Gebiete 65, 599–625 (1984). https://doi.org/10.1007/BF00531841
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DOI: https://doi.org/10.1007/BF00531841