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Teor. Veroyatnost. i Primenen., 2004, Volume 49, Issue 1, Pages 197–204 (Mi tvp247)  
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.

DOI: https://doi.org/10.4213/tvp247

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

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Received: 02.09.2002
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Citation: P. Eichelsbacher, “Refined large deviations for von Mises statistics”, Teor. Veroyatnost. i Primenen., 49:1 (2004), 197–204; Theory Probab. Appl., 49:1 (2005), 139–148

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