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Thresholding in Nonparametric Functional Regression with Scalar Response

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Recent Advances in Functional Data Analysis and Related Topics

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

In this work, we have focused on the nonparametric regression model with scalar response and functional covariate, and we have analyzed the existence of underlying complex structures in data by means of a thresholding procedure. Several thresholding functions are proposed, and a cross-validation criterion is used in order to estimate the threshold value. Furthermore, a simulation study shows the effectiveness of our method.

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References

  1. Ait-Saïdi, A., Ferraty, F., Kassa, R., Vieu, P.: Cross-validated estimations in the singlefunctional index model. Statistics 42 (6), 475–494 (2008)

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  2. Ferraty, F., Mas, A., Vieu, P.: Nonparametric regression on functional data: inference and practical aspects. Aust. N.Z. J. Stat. 49 (3), 267–286 (2007)

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  3. Ferraty, F., Vieu, P.:Nonparametric functional data analysis: theory and practice. Series in Statistics, Springer, New York (2006)

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  4. Ramsay, J. O., Silverman, B.W.: Functional Data Analysis (Second Edition). Springer Verlag, New York (2005)

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Correspondence to Frédéric Ferraty .

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© 2011 Springer-Verlag Berlin Heidelberg

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Ferraty, F., Martínez-Calvo, A., Vieu, P. (2011). Thresholding in Nonparametric Functional Regression with Scalar Response. In: Ferraty, F. (eds) Recent Advances in Functional Data Analysis and Related Topics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2736-1_16

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