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Uniform-in-bandwidth nearest-neighbor density estimation

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  • Ouadah, Sarah

Abstract

We present a sharp uniform-in-bandwidth limit law for the nearest-neighbor density estimator. Our result is established in the framework of convergence in probability, and we allow the bandwidth to vary within the complete range for which the estimator is consistent. We provide the explicit value of the asymptotic limiting constant for the uniform-in-bandwidth sup-norm of the estimator’s random error.

Suggested Citation

  • Ouadah, Sarah, 2013. "Uniform-in-bandwidth nearest-neighbor density estimation," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1835-1843.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:8:p:1835-1843
    DOI: 10.1016/j.spl.2013.04.014
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    References listed on IDEAS

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    1. Ralescu, S. S., 1995. "The Law of the Iterated Logarithm for the Multivariate Nearest Neighbor Density Estimators," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 159-179, April.
    2. Paul Deheuvels & David Mason, 2004. "General Asymptotic Confidence Bands Based on Kernel-type Function Estimators," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 225-277, October.
    3. Florent Burba & Frédéric Ferraty & Philippe Vieu, 2009. "-Nearest Neighbour method in functional nonparametric regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 453-469.
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    Cited by:

    1. Lydia Kara-Zaitri & Ali Laksaci & Mustapha Rachdi & Philippe Vieu, 2017. "Uniform in bandwidth consistency for various kernel estimators involving functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 85-107, January.
    2. Nengxiang Ling & Germán Aneiros & Philippe Vieu, 2020. "kNN estimation in functional partial linear modeling," Statistical Papers, Springer, vol. 61(1), pages 423-444, February.

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