We propose a family of robust nonparametric estimators for regression function based on kernel method. We establish the asymptotic normality of the estimator under the concentration properties on small balls of the probability measure of the functional explanatory dependent variables.
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References
Benner, P., Quintana-Ortí, E.S. and Quintana-Ortí, G.: Numerical solution of dis-crete stable linear matrix equations on multicomputers. Parallel Algorithms Appl. 17, 127-146 (2002).
Bosq, D.: Linear Processes in Function Spaces. Lecture Notes in Statistics. 149. Springer-Verlag, New-York (2000).
Cardot, H., Crambes, C., Kneip, A. and Sarda, P.: Smoothing spline estimators in functional linear regression with errors-in-variables. Comput. Statist. Data Anal. 51, 4832-4848 (2007).
Dierckx, P.: Curve and Surface Fitting with Splines. Oxford University Press, Oxford (1993).
Ferraty, F. and Vieu, P.: Nonparametric Functional Data analysis: Methods, Theory, Applications and Implementations. Springer-Verlag, London (2006).
He, G., Müller, H.G. and Wang, J.L.: Extending correlation and regression from multivariate to functional data.: In Asymptotics in Statistics and Probability. Ed. Puri, M.L., VSP International Science Publishers, 301-315 (2003).
Prchal, L. and Sarda, P.: Spline estimator for functional linear regression with func-tional response. Preprint. (2007).
Ramsay, J.O. and Dalzell, C.J.: Some tools for functional data analysis (with dis-cussion). J. R. Stat. Soc. Ser. B Stat. Methodol. 53, 539-572 (1991).
Ramsay, J.O. and Silverman, B.W.: Functional Data Analysis. 2nd edition. Springer, New York (2005).
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Attouch, M., Laksaci, A., Ould-Saïd, E. (2008). Asymptotic Normality of Robust Nonparametric Estimator for Functional Dependent Data. In: Functional and Operatorial Statistics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2062-1_5
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DOI: https://doi.org/10.1007/978-3-7908-2062-1_5
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-2061-4
Online ISBN: 978-3-7908-2062-1
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