Summary
A Berry-Essen result and asymptotic expansions are derived for the distribution of bivariate von Mises functionals under moment and smoothness conditions.
The results apply to the Cramér-von Mises ω 2 — statistic as well as to the Central Limit Theorem in Hilbert space, yielding a convergence rate O(n −1+ɛ) for every ɛ>0 on centered ellipsoids.
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Herrn Professor Dr. Leopold Schmetterer zu Ehren seines sechzigsten Geburtstages gewidmet
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Götze, F. Asymptotic expansions for bivariate von Mises functionals. Z. Wahrscheinlichkeitstheorie verw Gebiete 50, 333–355 (1979). https://doi.org/10.1007/BF00534154
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DOI: https://doi.org/10.1007/BF00534154