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An Empirical Process Approach to the Uniform Consistency of Kernel-Type Function Estimators

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  • Uwe Einmahl
  • David M. Mason

Abstract

We use general empirical process methods to determine under mild regularity conditions exact rates of uniform strong consistency of kernel-type function estimators. In the process a useful new bound on the expectation of the supremum of the empirical process is obtained

Suggested Citation

  • Uwe Einmahl & David M. Mason, 2000. "An Empirical Process Approach to the Uniform Consistency of Kernel-Type Function Estimators," Journal of Theoretical Probability, Springer, vol. 13(1), pages 1-37, January.
    • Handle: RePEc:spr:jotpro:v:13:y:2000:i:1:d:10.1023_a:1007769924157
    DOI: 10.1023/A:1007769924157
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    References listed on IDEAS

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    1. Einmahl, John H. J., 1997. "Poisson and Gaussian approximation of weighted local empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 31-58, October.
    2. Deheuvels, Paul, 1992. "Functional laws of the iterated logarithm for large increments of empirical and quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 133-163, November.
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    Cited by:

    1. Salim Bouzebda & Thouria El-hadjali & Anouar Abdeldjaoued Ferfache, 2023. "Uniform in Bandwidth Consistency of Conditional U-statistics Adaptive to Intrinsic Dimension in Presence of Censored Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1548-1606, August.
    2. Paul Deheuvels & Sarah Ouadah, 2013. "Uniform-in-Bandwidth Functional Limit Laws," Journal of Theoretical Probability, Springer, vol. 26(3), pages 697-721, September.
    3. Bianchi, Pascal & Elgui, Kevin & Portier, François, 2023. "Conditional independence testing via weighted partial copulas," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    4. D’Haultfœuille, Xavier & Hoderlein, Stefan & Sasaki, Yuya, 2023. "Nonparametric difference-in-differences in repeated cross-sections with continuous treatments," Journal of Econometrics, Elsevier, vol. 234(2), pages 664-690.
    5. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximation of suprema of empirical processes," CeMMAP working papers CWP44/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Fuqing Gao, 2003. "Moderate Deviations and Large Deviations for Kernel Density Estimators," Journal of Theoretical Probability, Springer, vol. 16(2), pages 401-418, April.
    7. Salim Bouzebda & Yousri Slaoui, 2023. "Nonparametric Recursive Estimation for Multivariate Derivative Functions by Stochastic Approximation Method," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 658-690, February.

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