VON MISES ω^{2}-STATISTIC AND THE GENERALIZED BAYESIAN BOOTSTRAPS

ALBERT Y. LO^{1} AND V. V. SAZONOV^{2}

1Department of Information and Systems Management, The Hong Kong University

of Science and Technology, Clear Water Bay, Hong Kong 2Steklov 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 ω^{2}-statistic for sampling from a continuous distribution and of the “generalized Bayesian ω^{2}-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.