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The Functional Nonparametric Model and Application to Spectrometric Data

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  • Frédéric Ferraty

    (Université Paul Sabatier
    Université Toulouse Le Mirail)

  • Philippe Vieu

    (Université Paul Sabatier)

Abstract

Summary The aim of this paper is to present a nonparametric regression model with scalar response when the explanatory variables are curves. In this context, the crucial problem of dimension reduction is overriden by the use of an implicit fractal dimension hypothesis. For such a functional nonparametric regression model we introduce and study both practical and theoretical aspects of some kernel type estimator. After a simulation study, it is shown how this procedure is well adapted to some spectrometric data set. Asymptotic results are described and in conclusion it turns out that this method combines advantages of easy implementation and good mathematical properties.

Suggested Citation

  • Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    • Handle: RePEc:spr:compst:v:17:y:2002:i:4:d:10.1007_s001800200126
    DOI: 10.1007/s001800200126
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    References listed on IDEAS

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    1. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    2. Brown P.J. & Fearn T & Vannucci M, 2001. "Bayesian Wavelet Regression on Curves With Application to a Spectroscopic Calibration Problem," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 398-408, June.
    3. Vicente Núñez-Antón & Juan Rodríguez-Póo & Philippe Vieu, 1999. "Longitudinal data with nonstationary errors: a nonparametric three-stage approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 201-231, June.
    4. M. C. Denham & P. J. Brown, 1993. "Calibration with Many Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(3), pages 515-528, September.
    5. Besse, Philippe C. & Cardot, Herve & Ferraty, Frederic, 1997. "Simultaneous non-parametric regressions of unbalanced longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 255-270, May.
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