Lo, Albert Y.; Sazonov, V. V. Von Mises \(\omega^ 2\)-statistic and the generalized Bayesian bootstraps. (English) Zbl 0890.62036 Ann. Inst. Stat. Math. 49, No. 1, 25-34 (1997). 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 Keywords:von Mises statistic; central limit theorem in Hilbert space; rate of approximation; uniform distance; uniform distribution; generalized Bayesian bootstrap PDF BibTeX XML Cite \textit{A. Y. Lo} and \textit{V. V. Sazonov}, Ann. Inst. Stat. Math. 49, No. 1, 25--34 (1997; Zbl 0890.62036) Full Text: DOI