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Moderate deviations for degenerate U-processes

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  • Eichelsbacher, Peter

Abstract

Sufficient conditions for a rank-dependent moderate deviations principle (MDP) for degenerate U-processes are presented. The MDP for VC classes of functions is obtained under exponential moments of the envelope. Among other techniques, randomization, decoupling inequalities and integrability of Gaussian and Rademacher chaos are used to present new Bernstein-type inequalities for U-processes which are the basis of our proofs of the MDP. We present a complete rank-dependent picture. The advantage of our approach is that we obtain in the degenerate case moderate deviations in non-Gaussian situations.

Suggested Citation

  • Eichelsbacher, Peter, 2000. "Moderate deviations for degenerate U-processes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 255-279, June.
    • Handle: RePEc:eee:spapps:v:87:y:2000:i:2:p:255-279
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    References listed on IDEAS

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    1. Arcones, Miguel A. & Giné, Evarist, 1995. "On the law of the iterated logarithm for canonical U-statistics and processes," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 217-245, August.
    2. Eichelsbacher, Peter, 1998. "Moderate and large deviations for U-processes," Stochastic Processes and their Applications, Elsevier, vol. 74(2), pages 273-296, June.
    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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