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The Law of the Iterated Logarithm for U-Processes

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  • Arcones, M. A.

Abstract

Sufficient conditions for the law of the iterated logarithm for non-degenerate U-processes are presented. The law of the iterated logarithm for V-C subgraph classes of functions is obtained under second moment of the envelope. A bracketing condition for the law of the iterated logarithm for U-processes is presented. Applications to the law of the iterated logarithm of U-statistics with estimated parameters and M-estimators are mentioned.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:47:y:1993:i:1:p:139-151
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    Cited by:

    1. Chen, Songnian, 2018. "Sequential estimation of censored quantile regression models," Journal of Econometrics, Elsevier, vol. 207(1), pages 30-52.
    2. Kaoukeb Turki-Moalla, 1998. "Rates of Convergence and Law of the Iterated Logarithm for U-Processes," Journal of Theoretical Probability, Springer, vol. 11(4), pages 869-906, October.
    3. Chen, Songnian & Wang, Qian, 2023. "Quantile regression with censoring and sample selection," Journal of Econometrics, Elsevier, vol. 234(1), pages 205-226.
    4. 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.
    5. Eichelsbacher, Peter, 1998. "Moderate and large deviations for U-processes," Stochastic Processes and their Applications, Elsevier, vol. 74(2), pages 273-296, June.
    6. Wendler, Martin, 2012. "U-processes, U-quantile processes and generalized linear statistics of dependent data," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 787-807.

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