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Rank-dependent moderate deviations of U-empirical measures in strong topologies
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  • Published: May 2003

Rank-dependent moderate deviations of U-empirical measures in strong topologies

  • Peter Eichelsbacher1 &
  • Uwe Schmock2 

Probability Theory and Related Fields volume 126, pages 61–90 (2003)Cite this article

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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Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität Bochum, Gebäude NA 3/68, D-44780 Bochum, Germany. e-mail: peter.eichelsbacher@ruhr-uni-bochum.de, , , , , , DE

    Peter Eichelsbacher

  2. Departement Mathematik, ETH Zentrum, HG F42.1, CH-8092 Zürich, Switzerland. e-mail: schmock@math.ethz.ch; http://www.math.ethz.ch/∼schmock/, , , , , , CH

    Uwe Schmock

Authors
  1. Peter Eichelsbacher
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  2. Uwe Schmock
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Additional information

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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  • Issue Date: May 2003

  • DOI: https://doi.org/10.1007/s00440-003-0254-6

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Keywords

  • Rate Function
  • Moderate Deviation
  • Degenerate Case
  • Deviation Principle
  • Strong Topology
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