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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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