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-Nearest Neighbour method in functional nonparametric regression

Author

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  • Florent Burba
  • Frédéric Ferraty
  • Philippe Vieu

Abstract

The aim of this article is to study the k-nearest neighbour (kNN) method in nonparametric functional regression. We present asymptotic properties of the kNN kernel estimator: the almost-complete convergence and its rate. Then, we illustrate the effectiveness of this method by comparing it with the traditional kernel approach first on simulated datasets and then on a real chemometrical example. We also present in this article an important technical tool which could be useful in many other situations than ours.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:453-469
    DOI: 10.1080/10485250802668909
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    Cited by:

    1. Boente, Graciela & Vahnovan, Alejandra, 2015. "Strong convergence of robust equivariant nonparametric functional regression estimators," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 1-11.
    2. Timmermans, Catherine & Delsol, Laurent & von Sachs, Rainer, 2011. "Using Bagidis in nonparametric functional data analysis: predicting from curves with sharp local features," LIDAM Discussion Papers ISBA 2011020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    4. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.
    5. Carlo Sguera & Pedro Galeano & Rosa Lillo, 2014. "Spatial depth-based classification for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 725-750, December.
    6. Kudraszow, Nadia L. & Vieu, Philippe, 2013. "Uniform consistency of kNN regressors for functional variables," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1863-1870.
    7. Ouadah, Sarah, 2013. "Uniform-in-bandwidth nearest-neighbor density estimation," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1835-1843.
    8. Epifanio, Irene & Ventura-Campos, Noelia, 2011. "Functional data analysis in shape analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2758-2773, September.

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