Rank-Dependent Moderate Deviations of U-Empirical Measures in Strong Topologies

Peter Eichelsbacher and Uwe Schmock

Abstract: We prove a rank-dependent moderate deviation principle for U-empirical measures, where the underlying i.i.d. random variables take values in a measurable (not necessarily Polish) space S. The result can be formulated on a suitable subset of all signed measures on the product space Sm. We endow this space with a topology, which is stronger than the usual tau-topology. A moderate deviation principle for Banach-space valued U-statistics is obtained as a particular application. The advantage of our result is that we obtain in the degenerate case moderate deviations in non-Gaussian situations with non-convex rate functions.

Keywords: rank-dependent moderate deviations, empirical measures, strong topology, U-statistics

Reference: Probability Theory and Related Fields, Volume 126, Number 1, Pages 61-90 (2003)

DOI: 10.1007/s00440-003-0254-6

Copyright: Springer-Verlag

2010 Mathematics Subject Classification:

The paper (27 pages, final version February 27, 2003) is available in:

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