Optimal asymptotic quadratic error of nonparametric regression function estimates for a continuous-time process from sampled-data

Statistics

Volumn 32, Issue 3, 1999, Pages 229-247

  Bosq, Denis ^a   Cheze Payaud, Nathalie ^b,c  

^a SORBONNE UNIVERSITÉ   (France)

^b UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

^c Universite Paris X ^*  (France)

Author keywords

Choice of bandwidth; Mixing continuous parameter processes; Nonparametric regression estimation; Quadratic mean convergence; Sampled data

Indexed keywords

EID: 0346347829     PISSN: 02331888     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331889908802665     Document Type: Article

References (31)

1. Ango Nze, P. and Portier, P. (1994). Estimation of the density and of the regression functions of an absolutely regular stationary process, Publications de l'I.S.U.P. XXXVIII, fasc. 2, 59-88.
2. Banon, G. (1978). Nonparametric identification for diffusion processes. Siam Journal Control and Opt., 16(3), 380-395.
3. Banon, G. and Nguyen, H. T. (1981). Recursive estimation in diffusion model, Siam Journal Control and Opt., 19, 676-685.
4. Berlinet, A. and Devroye, L. (1994). A comparison of kernel density estimates, Publications de l'I.S.U.P. XXXVIII, fasc. 3, 3-60.
5. Beutler (1970). Alias-Free Randomly Timed sampling of Stochastic Processes, IEEE Trans. Inf. Th., 16(2), 147-152.
6. Bosq, D. and Lecoutre, J. P. (1987). Théorie de l'estimation fonctionnelle, Economica, Paris.
7. Bosq, D. (1987). Bernstein-type large deviations inequalities for partial sums of strong mixing processes, Statistics, 24, 59-70.
8. Bosq, D. (1993). Erreur quadratique optimale pour les estimateurs à noyau de la densité et de la régression d'un processus mélangeant, C. R. Acad. Sci., Paris, t.316, Ser. I, 293-295.
9. Bosq, D. and Cheze, N. (1993). Erreur quadratique asymptotique optimale de l'estimateur non paramétrique de la régression pour des observations discrétisées, C. R. Acad. Sci., Paris, t.317, Ser. A, 891-894.
10. Cambanis, S. and Masry, E. (1988). Performance of discrete-time predictors of continuous time stationary processes, IEEE Trans. Inf. Th., 34, 655-668.
11. Castellana, J. V. and Leadbetter, M. R. (1986). On smoothed probability density estimation for stationary processes, Stoch. Proc. Appl., 21, 179-193.
12. Cheze-Payaud, N. (1992). Régression non paramétrique pour un processus à temps continu, C. R. Acad. Sci., Paris, t.315, Ser. I, 1009-1012.
13. Cheze-Payaud, N. (1994). Nonparametric regression and prediction for continuous-time processes, Publications de l'I.S.U.P. XXXVIII, fasc. 2, 37-58.
14. Cheze-Payaud, N. (1994). Régression, prédiction and discrétisation des processus à temps continu, thèse de Doctorat de l'université Paris 6.
15. Collomb, G. and Doukhan, P. (1983). Estimation non paramétrique de la fonction d'autorégression d'un processus stationnaire φ-mélangeant: risque quadratique par la méthode de noyau, C. R. Acad. Sci., Paris, t.296, Ser. I, 859-862.
16. Deheuvels, P. and Hominal, Estimation non paramétrique de la densité par histogrammes généralisés, bf 1977, Revue de Statistique Appliquée, 25, 5-42.
17. Delecroix, M., Sur l'estimation des densites d'un processus stationnaire à temps continu, bf 1980, Publications de l'I.S.U.P. XXV, fasc. 1-2, 17-39.
18. Doe, C. M. (1973). A note on empirical processes for strong mixing processes, Ann. Prob., I, 870-875.
19. Doukhan, P. (1991). Consistency of delta-sequence estimates of a density or of a regression function for a weakly stationary sequence, Prépublications mathématiques de l'Universitié d' Orsay 9155.
20. Doukhan, P. (1994). Mixing, Properties and examples, Lecture Notes in Statistics, 72, Springer-Verlag.
21. Härdle, W., Hall, P. and Marron, J. S. (1988). How far are automatically chosen regression smoothing parameter from their optimum. J. Amer. Statist. Assoc., 83, 401, 86-101.
22. Härdle, W. (1990). Applied Nonparametric Regression, Cambridge University Press, Econometric Society Monograph Series 19.
23. Leblanc, F. (1995). Thèse de Doctorat de l'université Paris 6.
24. Masry, E. (1978). Poisson-sampling and spectral estimation of continuous-time processes, IEEE Trans. Inf. Th., 24, 173-183.
25. Masry, E. (1983). Probability density estimation from sampled-data, IEEE Trans Inf. Th., 29, 696-709.
26. Masry, E. (1983). Nonparametric covariance estimation from irregularly spaced data, Adv. Appl. Prob., 15, 113-132.
27. Nguyen, H. T. and Pham, T. D., Nonparametric estimation in diffusion model dy discrete-sampling, bf 1981, Publications de l'I.S.U.P., XXVI, fasc. 2, 89-109.
28. Prakasa Rao, B. L. S. (1990). Nonparametric density estimation for stochastic process from sampled-data, Publications de l'I.S.U.P. XXXV, pp. 51-84.
29. Rhomari, N. (1994). Thése de Doctorat de l'université Paris 6.
30. Rosenblatt, M. (1969). Conditional probability density and regression estimators, Multivariate Analysis, II, 25-31, Academic Press, New York.
31. Stone, C. J. and Truong, Y. K. (1992). Nonparametric function estimation involving time series, Annals of Stat., 20(1), 77-97.