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The central limit theorem for U-processes indexed by Hölder's functions

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  • Arcones, Miguel A.

Abstract

Let . It is shown that the condition , which is known to be equivalent to 1 being P-Donsker, implies that [alpha] is P-Donsker for . U-processes indexed by these classes of Hölder's functions are also considered.

Suggested Citation

  • Arcones, Miguel A., 1994. "The central limit theorem for U-processes indexed by Hölder's functions," Statistics & Probability Letters, Elsevier, vol. 20(1), pages 57-62, May.
    • Handle: RePEc:eee:stapro:v:20:y:1994:i:1:p:57-62
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    Cited by:

    1. Richard Nickl & Benedikt M. Pötscher, 2007. "Bracketing Metric Entropy Rates and Empirical Central Limit Theorems for Function Classes of Besov- and Sobolev-Type," Journal of Theoretical Probability, Springer, vol. 20(2), pages 177-199, June.
    2. Cizek, P., 2007. "General Trimmed Estimation : Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaces DP 2007-1)," Other publications TiSEM eeccf622-dd18-41d4-a2f9-b, Tilburg University, School of Economics and Management.
    3. Pavel Čížek, 2013. "Reweighted least trimmed squares: an alternative to one-step estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 514-533, September.
    4. Chung-Ming Kuan & Christos Michalopoulos & Zhijie Xiao, 2017. "Quantile Regression on Quantile Ranges – A Threshold Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(1), pages 99-119, January.
    5. Arcones, Miguel A., 1996. "Weak convergence of stochastic processes indexed by smooth functions," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 115-138, March.
    6. Giné, Evarist & Wellner, Jon A., 1997. "Uniform convergence in some limit theorems for multiple particle systems," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 47-72, December.

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