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Moderate and large deviations for U-processes

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  • Eichelsbacher, Peter

Abstract

Sufficient conditions for the moderate and large deviation principle for U-processes are given. For the large deviation result the conditions are in terms of "blockwise" empirical process conditions. On the moderate scaling the case of U-processes indexed by a uniformly bounded VC subgraph class of functions is considered. The proofs are based on an isoperimetric inequality for empirical processes due to Talagrand, a truncation method based on an isoperimetric inequality by Ledoux, the existence of almost regular partitions of complete hypergraphs due to Baranyai and a Bernstein-type inequality for U-processes due to Arcones and Giné.

Suggested Citation

  • Eichelsbacher, Peter, 1998. "Moderate and large deviations for U-processes," Stochastic Processes and their Applications, Elsevier, vol. 74(2), pages 273-296, June.
    • Handle: RePEc:eee:spapps:v:74:y:1998:i:2:p:273-296
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    References listed on IDEAS

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    1. Arcones, Miguel A., 1995. "A Bernstein-type inequality for U-statistics and U-processes," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 239-247, February.
    2. Arcones, M. A., 1993. "The Law of the Iterated Logarithm for U-Processes," Journal of Multivariate Analysis, Elsevier, vol. 47(1), pages 139-151, October.
    3. Arcones, Miguel A. & Giné, Evarist, 1994. "U-processes indexed by Vapnik-Cervonenkis classes of functions with applications to asymptotics and bootstrap of U-statistics with estimated parameters," Stochastic Processes and their Applications, Elsevier, vol. 52(1), pages 17-38, August.
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    1. Eichelsbacher, Peter, 2000. "Moderate deviations for degenerate U-processes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 255-279, June.

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