Estimating some characteristics of the conditional distribution in nonparametric functional models

Statistical Inference for Stochastic Processes

Volumn 9, Issue 1, 2006, Pages 47-76

  Ferraty, Frédéric ^a   Laksaci, Ali ^b   Vieu, Philippe ^c  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b UNIVERSITY OF SIDI BEL ABBES   (Algeria)

^c UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Conditional cumulative distribution; Conditional mode; Conditional quantile; Derivatives of conditional density; Diffusion processes; Functional random variable; Gaussian processes; Kernel estimator; Nonparametric estimation; Small ball probability

Indexed keywords

EID: 33646504887     PISSN: 13870874     EISSN: 15729311     Source Type: Journal    
DOI: 10.1007/s11203-004-3561-3     Document Type: Article

References (33)

1. Banon, G.: Nonparametric identification for diffusion processes, Siam. Journ. Control and Optim. 16 (1978), 380-395.
2. Berlinet, A., Gannoun, A. and Matzner-Lober, E.: Normalité asymptotique d'estimateurs convergents du mode conditionnel (French), La Rev. Canad. de Statist. 26 (1998), 365-380.
3. Berlinet, A., Gannoun, A. and Matzner-Lober, E.: Asymptotic normality of convergent estimates of conditional quantiles, Statistics 35 (2001), 139-169.
4. Besse, P., Cardot, H. and Stephenson, D.: Autoregressive forecasting of some functional climatic variations, Scand. J. of Statist. 27 (2000), 673-687.
5. Bogachev, V. I.: Gaussian measures. Math surveys and monographs, 62, (1999), Amer. Math. Soc.
6. Bosq, D.: Linear processs in function spaces, Lecture Notes in Statistics, Vol. 149, Springer-Verlag, 2000.
7. 1-median of a Banach valued random variable, Statistics (2001), 509-521.
8. Collomb, G., Hardle, W. and Hassani, S.: A note on prediction via conditional mode estimation, J. Statist. Plann. and Inf. 15 (1987), 227-236.
9. Damon, J. and Guillas, S.: The inclusion of exogeneous variables in functional autoregressive ozone forecasting, Environmetrics 13 (2002), 2487-2500.
10. Fernández de Castro, B. Guillas, S. and Gonzalez Manteiga, W.: Functional samples and bootstrap for the prediction of SO2 levels, (2003), Preprint.
11. Ferraty, F., Goia, A. and Vieu, P.: Functional nonparametric model for time series: a fractal approach to dimension reduction. TEST 11 (2002), 317-344.
12. Ferraty, F and Vieu, P.: Dimension fractale et estimation de la regression dans des espaces vectoriels semi-normés, Compte Rendus Acad. Sci. Paris 330 (2000), 403-406.
13. Ferraty, F. and Vieu, P.: The functional nonparametric model and application to spectrometric data, Comput. Stat. 4 (2002), 545-564.
14. Ferraty, F. and Vieu, P.: Curves discrimination: a nonparametric functional approach, Computational Statistics and Data Analysis 44 (2003), 161-173.
15. Ferraty, F and Vieu, P.: Functional nonparametric statistics: A double infinite dimensional framework. In: M. Akritas and D. Politis Current Advances and Trends in Nonparametric Statistics Elsevier, (2003), 61-79.
16. Ferraty, F. and Vieu, P.: Nonparametric models for functional data, with applications in regression, time series prediction and curves discrimination. J. Nonparametric Stat. 16 (2004), 111-127.
17. Gasser, T. Hall, P. and Presnell, B.: Nonparametric estimation of the mode of a distribution of random curves, J. R. Statist. Soc. B 60 (1998), 681-691.
18. Hall, P. and Heckman, N.: Estimating and depicting the structure of the distribution of random functions, Biometrika 89 (2002), 145-158.
19. Hall, P., Poskitt, P. and Presnell, D.: A functional data-analytic approach to signal discrimination, Technometrics 35 (2001), 140-143.
20. Li, W. V. and Shao, Q. M.: Gaussian processes: inequalities, small ball probabilities and applications. In: Rao, C. R. and Shanbhag, D. (eds), Stochastic Processes: Theory and Methods, Hanbook of Statistics, Vol. 19 (2001), North-Holland, Amsterdam.
21. Louani, D. and Ould-Saïd, E.: Asymptotic normality of kernel estimators of the conditional mode under strong mixing hypothesis, J. of Nonparametric Statistics 11 (1999), 413-442.
22. Niang, S.: Estimation de la densité dans un espace de dimension infinie: Application aux diffusions (french), Comptes Rendus Acad. Sci. Paris, Ser. I 334 (2002), 213-216.
23. Niang, S.: Sur l'estimation fonctionnelle en dimension infinie: Application aux diffusions (french), PhD thesis, Paris 6, France, 2002b.
24. Quintela del Rio, A. and Vieu, P.: A nonparametric conditionnal mode estimate, Nonparametric Statistics 8 (1997), 253-266.
25. Ramsay, J. and Silverman, B.: Functional Data Analysis. Springer-Verlag, 1997.
26. Ramsay, J. and Silverman, B.: Appied functional Data Analysis. Springer-Verlag, 2002.
27. Rosenblatt, M.: Conditional probability density and regression estimators. In: P.R. Krishnaiah (eds.), Multivariate Analysis II, Acdaemic Press, New York and London, 1969.
28. Roussas, G.: Nonparametric estimation of the transition distribution function of a Markov process, Ann. Math. Statist. 40 (1969), 1386-1400.
29. Samanta, M.: Non-parametric estimation of conditional quantiles, Statist. Proba. Letters 7 (1989), 407-412.
30. Shi, Z.: Small ball probabilities for a Wiener process under weighted sup-norms, with an application to the supremum of Bessel local times, J. Theoret. Probab. 9 (1996), 915-929.
31. Staph: Proceedings of the working group on Functional Statistics: 2001-2002. Techn. report, Labo. Statist. Proba. Toulouse, France, 2002-2000 12 (2002). (Available on line at www.lsp.ups-tlse.fr/Fp/Ferraty/staph.html).
32. Uspensky, J. V.: Introduction to Mathematical Probability. McGraw-Hill Book Company, Inc., New York and London, 1937.
33. Youndjé, E.: Propriétés de convergence de l'estimateur à noyau de la densité conditionnelle (French), Rev. Roumaine Math. Pures Appl. 41 (1996), 535-566.