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Nonparametric regression for mixing functional random variables. (Régression non-paramétrique pour des variables aléatoires fonctionnelles mélangeantes.) (French) Zbl 0998.62036
Summary: This paper concerns a nonparametric regression model for dependent functional variables. The aim is to explain a r.r.v. \(Y\) by a functional regressor, namely a variable \(X\) which is valued in some semi-normed vector space. A kernel-type estimator is proposed and asymptotics with rates are proved under strong mixing assumptions.

MSC:
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
60B11 Probability theory on linear topological spaces
Software:
fda (R)
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References:
[1] Bosq, D., Nonparametric statistics for stochastic processes: estimation and prediction, Lecture notes in statist., 110, (1998), Springer-Verlag · Zbl 0902.62099
[2] Bosq, D., Linear processes in function spaces, Theory and applications, Lecture notes in statist., 149, (2000), Springer-Verlag
[3] Ferraty, F.; Vieu, P., Dimension fractale et estimation de la régression dans des espaces vectoriels semi-normés, C. R. acad. sci. Paris, 330, 139-142, (2000) · Zbl 0942.62045
[4] F. Ferraty, P. Vieu, The functional nonparametric model and application to spectrometric data, Comput. Statist. (2001) (a paraı̂tre) · Zbl 1037.62032
[5] F. Ferraty, A. Goia, P. Vieu, Functional nonparametric model for time series: a fractal approach for dimension reduction, Preprint, 2001 · Zbl 1020.62089
[6] Ramsay, J.O.; Silverman, B.W., Functional data analysis, (1997), Springer-Verlag · Zbl 0882.62002
[7] Rio, E., Théorie asymptotique des processus faiblement dépendants, Mathématiques & applications, 31, (1999), Springer-SMAI
[8] STAPH, Statistique Fonctionnelle : résumés des exposés 1999-2000, Publication du Laboratoire de Statistique et Probabilités de Toulouse, #LSP-2001-05, 2000
[9] STAPH, Statistique Fonctionnelle : résumés des exposés 2000-2001, Publication du Laboratoire de Statistique et Probabilités de Toulouse, #LSP-2001-07, 2001
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