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U-processes indexed by Vapnik-Cervonenkis classes of functions with applications to asymptotics and bootstrap of U-statistics with estimated parameters

Author

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  • Arcones, Miguel A.
  • Giné, Evarist

Abstract

Exponential inequalities, the law of the iterated logarithm and the bootstrap central limit theorem for U-processes indexed by Vapnik-Cervonenkis classes of functions are derived. These results are then applied to the asymptotics and the bootstrap of U-statistics with estimated parameters, in particular to the trimming of U-statistics.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:52:y:1994:i:1:p:17-38
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    Citations

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    Cited by:

    1. Yoshihiko Nishiyama & Peter M. Robinson, 2005. "The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 73(3), pages 903-948, May.
    2. Eichelsbacher, Peter, 2000. "Moderate deviations for degenerate U-processes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 255-279, June.
    3. Subbotin, Viktor, 2007. "Asymptotic and bootstrap properties of rank regressions," MPRA Paper 9030, University Library of Munich, Germany, revised 20 Mar 2008.
    4. Pedro Delicado & Juan Romo, 1998. "Constant coefficient tests for random coefficient regression," Economics Working Papers 329, Department of Economics and Business, Universitat Pompeu Fabra.
    5. 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.
    6. Subbotin, Viktor, 2008. "Essays on the econometric theory of rank regressions," MPRA Paper 14086, University Library of Munich, Germany.
    7. Eichelsbacher, Peter, 1998. "Moderate and large deviations for U-processes," Stochastic Processes and their Applications, Elsevier, vol. 74(2), pages 273-296, June.

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