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Uniform consistency of kNN regressors for functional variables

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  • Kudraszow, Nadia L.
  • Vieu, Philippe

Abstract

This paper is devoted to nonparametric analysis of functional data. We give asymptotic results for a kNN generalized regression estimator when the observed variables take values in any abstract space. The main novelty is our uniform consistency result (with rates).

Suggested Citation

  • Kudraszow, Nadia L. & Vieu, Philippe, 2013. "Uniform consistency of kNN regressors for functional variables," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1863-1870.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:8:p:1863-1870
    DOI: 10.1016/j.spl.2013.04.017
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    References listed on IDEAS

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    1. K. Benhenni & F. Ferraty & M. Rachdi & P. Vieu, 2007. "Local smoothing regression with functional data," Computational Statistics, Springer, vol. 22(3), pages 353-369, September.
    2. M'hamed Ezzahrioui & Elias Ould-Saïd, 2008. "Asymptotic normality of a nonparametric estimator of the conditional mode function for functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(1), pages 3-18.
    3. Bhattacharya, P. K. & Mack, Y. P., 1990. "Multivariate data-driven k-NN function estimation," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 1-11, October.
    4. Biau, Gérard & Devroye, Luc, 2010. "On the layered nearest neighbour estimate, the bagged nearest neighbour estimate and the random forest method in regression and classification," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2499-2518, November.
    5. 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.
    Full references (including those not matched with items on IDEAS)

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