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,𝒮). The result can be formulated on a suitable subset of all signed measures on (S m,𝒮⊗ m). We endow this space with a topology, which is stronger than the usual τ-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.
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Received: 22 February 2000 / Revised version: 15 November 2002 / Published online: 28 March 2003
Research partially supported by the Swiss National Foundation, Contract No. 21-298333.90.
Mathematics Subject Classification (2000): Primary 60F10; Secondary 62G20, 28A35
Key words or phrases: Rank-dependent moderate deviations – Empirical measures – Strong topology – U-statistics
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Eichelsbacher, P., Schmock, U. Rank-dependent moderate deviations of U-empirical measures in strong topologies. Probab. Theory Relat. Fields 126, 61–90 (2003). https://doi.org/10.1007/s00440-003-0254-6
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DOI: https://doi.org/10.1007/s00440-003-0254-6
Keywords
- Rate Function
- Moderate Deviation
- Degenerate Case
- Deviation Principle
- Strong Topology