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Short Communications

Refined large deviations for von Mises statistics

P. Eichelsbacher

Ruhr-Universität Bochum

Abstract: We give sufficient conditions for the large deviations principle of real valued von Mises statistics, improving previous results. As a consequence we obtain sufficient conditions for the large deviations principle for Banach space valued $U$-statistics, improving previous results as well. The proofs are based on large deviations results for stochastic processes due to Arcones and a spectral decomposition of the kernel function of the von Mises statistic and the $U$-statistic, respectively.

Keywords: large deviations, $U$-statistics, von Mises statistics, stochastic processes.

Received: 02.09.2002

Language: English

DOI: 10.4213/tvp247

 English version: Theory of Probability and its Applications, 2005, 49:1, 139–148

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