VON MISES omega2-STATISTIC AND THE GENERALIZED
BAYESIAN BOOTSTRAPS

ALBERT Y. LO 1 AND V. V. SAZONOV 2

1 Department of Information and Systems Management, The Hong Kong University
of Science and Technology, Clear Water Bay, Hong Kong
2 Steklov Mathematical Institute, Russian Academy of Sciences,
42 Vavilov Street, 117966 Moscow, Russia

(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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