(Received June 26, 1995; revised April 22, 1996)
Abstract. The uniform distance between the distribution functions of the von Mises omega2-statistic for sampling from a continuous distribution and of the ``generalized Bayesian omega2-statistic'' for sampling from the uniform distribution on a finite number of points is estimated. Application to the generalized Bayesian bootstraps is discussed.
Key words and phrases: von Mises statistic, Bayesian bootstrap, central limit theorem in Hilbert space, rate of approximation.
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