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Bracketing smooth functions

Author

Listed:
  • van der Vaart, Aad

Abstract

Let be the class of functions which are [alpha] times differentiable with derivatives bounded by numbers Mj on each given set Ij in a partition of . We obtain upper and lower bounds on the Lr(P)-bracketing entropy of .

Suggested Citation

  • van der Vaart, Aad, 1994. "Bracketing smooth functions," Stochastic Processes and their Applications, Elsevier, vol. 52(1), pages 93-105, August.
    • Handle: RePEc:eee:spapps:v:52:y:1994:i:1:p:93-105
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    Citations

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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. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    3. 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.
    4. Yuehao Bai & Jizhou Liu & Azeem M. Shaikh & Max Tabord-Meehan, 2023. "On the Efficiency of Finely Stratified Experiments," Papers 2307.15181, arXiv.org, revised Feb 2024.
    5. 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.
    6. Bertille Antoine & Pascal Lavergne, 2020. "Identification-Robust Nonparametric Interference in a Linear IV Model," Discussion Papers dp20-03, Department of Economics, Simon Fraser University.

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