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Von Mises $$\omega^ 2$$-statistic and the generalized Bayesian bootstraps. (English) Zbl 0890.62036
Summary: The uniform distance between the distribution functions of the von Mises $$\omega^2$$-statistic for sampling from a continuous distribution and of the “generalized Bayesian $$\omega^2$$-statistic” for sampling from the uniform distribution on a finite number of points is estimated. Application to the generalized Bayesian bootstrap is discussed.
##### MSC:
 62G09 Nonparametric statistical resampling methods 60F05 Central limit and other weak theorems 62G20 Asymptotic properties of nonparametric inference 46N30 Applications of functional analysis in probability theory and statistics
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