The Functional Nonparametric Model and Application to Spectrometric Data
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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.
KeywordsDimension Reduction Functional Data Nonparametric Estimate Regression Model Spectrometric Data
The authors wish to thank Professor D. Tjøstheim both for interesting discussions and careful proofreading of this manuscript, Professor Holik for helpful comments about chemometrical aspects of our study and Professor D. Stephenson for pertinent remarks. The encouragements of Hervé Cardot and Pascal Sarda, and more generally those of all the participants of the working group STAPH on Statistique Fonctionnelle of our department, are gratefully acknowledged. This paper has also been greatly improved by the helpful comments of the Editor, the Associate Editor and the referees.
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