Rates of strong consistencies of the regression function estimator for functional stationary ergodic data

Journal of Statistical Planning and Inference

Volumn 141, Issue 1, 2011, Pages 359-372

  Laib, Naâmane ^a   Louani, Djamal ^a  

^a University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

Author keywords

Ergodic processes; Functional data; Martingale difference; Primary, 62G07; Rate of convergence; Regression estimation; Secondary, 62M09; Strong consistency; Vapnik Chervonenkis class

Indexed keywords

EID: 77956277945     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2010.06.009     Document Type: Article

References (18)

1. Bosq D. Nonparametric Statistics for Stochastic Processes. Lecture Note in Statistics 1998, Springer, New York.
2. Bosq, D., 2000. Linear Processes in Function Spaces, Theory and Applications, Lecture Notes in Statistics, vol. 149. Springer-Verlag, New York, Berlin, Heidelberg.
3. de la Peña V.H., Giné E. Decoupling from Dependence to Independence. Probability and its Applications 1999, Springer-Verlag, New York.
4. Delsol L. Advances on asymptotic normality in non-parametric functional time series analysis. Statistics 2009, 43:13-33.
5. Ezzahrioui M., Ould-Saïd E. Asymptotic normality of a nonparametric estimator of the conditional mode function for functional data. J. Nonparametric. Statist. 2008, 20:3-18.
6. Ferraty F., Vieu P. Dimension fractale et estimation de la régression dans des espaces vectoriels semi-normés. C. R. Acad. Sci. Paris Sér. I Math. 2000, 330:139-142.
7. Ferraty F., Goia A., Vieu P. Functional nonparametric model for time series: a fractal approach for dimension reduction. Test 2002, 11(2):317-344.
8. Ferraty F., Vieu P. Nonparametric models for functional data, with applications in regression, time series prediction and curve discrimination. The international conference on recent trends and directions in nonparametric statistics. J. Nonparametric Statist. 2004, 16:111-125.
9. Ferraty F., Vieu P. Nonparametric Functional Data Analysis. Theory and Practice. Springer Series in Statistics 2006, Springer, New York.
10. Ferraty F., Mass A., Vieu P. Nonparametric regression of functional data: inference and practical aspects. Aust. N. Z. J. Statist. 2007, 49:267-286.
11. Gasser T., Hall P., Presnell B. Nonparametric estimation of the mode of a distribution of random curves. J. Roy. Statist. Soc. Ser. B 1998, 60:681-691.
12. Laïb, N., Louani, D., 2010. Nonparametric kernel regression estimation for functional stationary ergodic data: asymptotic properties. J. Multivariate Anal., in press.
13. Li, W.V., Shao, Q.-M., 2001. Gaussian processes: inequalities, small ball probabilities and applications. In: Stochastic Processes: Theory and Methods, Handbook of Statistics, vol. 19, North-Holland, Amsterdam, pp. 533-597.
14. Lipster R.S., Shiryayev A.N. On the absolute continuity of measures corresponding to processes of diffusion type relative to a Wiener measure. Izv. Akad. Nauk. Ser. Mat. 1972, 36:839-882.
15. Masry E. Nonparametric regression estimation for dependent functional data: asymptotic normality. Stochastic Process. Appl. 2005, 115:155-177.
16. Ramsay J., Silverman B.W. Functional Data Analysis 1997, Springer, New York.
17. Ramsay J., Silverman B.W. Applied Functional Data Analysis: Methods and Case Studies 2002, Springer, New York.
18. van der Vaart A.W., Wellner J.A. Weak Convergence and Empirical Processes. With Applications to Statistics. Springer Series in Statistics 1996, Springer-Verlag, New York.