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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. 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.
    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. Ouadah, Sarah, 2013. "Uniform-in-bandwidth nearest-neighbor density estimation," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1835-1843.
    6. Epifanio, Irene & Ventura-Campos, Noelia, 2011. "Functional data analysis in shape analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2758-2773, September.
    7. 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).
    8. Kudraszow, Nadia L. & Vieu, Philippe, 2013. "Uniform consistency of kNN regressors for functional variables," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1863-1870.

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