Asymptotic expansions for bivariate von Mises functionals

SummaryA 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 ω2 — 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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