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The functional nonparametric model and applications to spectrometric data. (English) Zbl 1037.62032
The goal of this paper is to introduce and study a nonparametric regression model with scalar response when explanatory variables are curves. The problem of regression estimation is reformulated in terms of a general regression model in a semi-normed vector space and kernel smoothing ideas are used. So, the authors construct nonparametric estimates based on convolution kernel ideas and propose a practical automatic procedure that provides an easy computation scheme and deal with the optimality problem. After a simulation study this procedure is applied to real spectrometric data and demonstrates good performance. Finally, asymptotic results with rates of uniform almost sure convergence are presented. Thus, it is shown that the proposed method successfully combines advantages of easy implementation and good mathematical properties.

62G08 Nonparametric regression and quantile regression
62G07 Density estimation
fda (R); KernSmooth; R
Full Text: DOI
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