no. 3-4
Statistics
Optimal and superoptimal convergence rate of the local linear estimator of nonparametric regression function in continuous time
[L'optimalité et la suroptimalité du lissage localement linéaire de la fonction de régression]

Présenté par : Paul Deveuvels

Shen, Jia1 ; Sun, Shuguang1
1 Department of Statistics, Fudan University, Shanghai 200433, China
Comptes Rendus. Mathématique, Tome 348 (2010) no. 3-4, pp. 211-215.

Nous étudions l'estimation non paramétrique de la fonction de régression par le lissage localement linéaire au sens d'erreur quadratique asymptotique. Sous des conditions de forte mélangeance et d'irrégularité, nous obtenons des vitesses de convergence optimale et suroptimale de l'estimateur pour l'erreur quadratique asymptotique.

We consider the estimation problem of the nonparametric regression in continuous time by the local linear estimator in the asymptotic quadratic error sense. In suitable conditions of strongly mixing and that of irregularity, we obtained optimal and superoptimal convergence rate of the estimator.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.12.005
Shen, Jia 1 ; Sun, Shuguang 1

1 Department of Statistics, Fudan University, Shanghai 200433, China 
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Shen, Jia; Sun, Shuguang. Optimal and superoptimal convergence rate of the local linear estimator of nonparametric regression function in continuous time. Comptes Rendus. Mathématique, Tome 348 (2010) no. 3-4, pp. 211-215. doi : 10.1016/j.crma.2009.12.005. http://www.numdam.org/articles/10.1016/j.crma.2009.12.005/

[1] Blanke, D. Estimation of local smoothness coefficients for continuous time processes, Stat. Inference Stoch. Process., Volume 5 (2002) no. 1, pp. 65-93

[2] Blanke, D.; Bosq, D. Regression estimation and prediction in continuous time, J. Japan Statist. Soc. (2008)

[3] Bosq, D. Parametric rates of noparametric estimators and predictors for continuous time processes, Ann. Statist., Volume 25 (1997) no. 3, pp. 982-1000

[4] Bosq, D. Nonparametric Statistics for Stochastic Processes, Lecture Notes in Statist., vol. 110, Springer-Verlag, New York, 1998

[5] Bosq, D.; Blanke, D. Inference and Prediction in Large Dimensions, Wiley Ser. Probab. Stat., vol. 754, Wiley-Dunod, Chichester, England, 2007

[6] Bosq, D.; Cheze, N. Erreur quadratique asymptotique optimale de l'estimateur non paramétrique de la régression pour des observations discrétisées d'un processus stationaire à temps continu, C. R. Acad. Sci., Paris Sér. I, Volume 317 (1993) no. 9, pp. 891-894

[7] Castellana, J.V.; Leadbetter, M.R. On smoothed probability density estimation or stationary processes, Stochastic Process. Appl., Volume 21 (1986), pp. 179-193

[8] Cheze, N. Régression non paramétrique pour un processus à temps continu, C. R. Acad. Sci., Paris Sér. I, Volume 315 (1992), pp. 1009-1012

[9] Nathalie Cheze–Payaud, Régression, prédiction et discrétisation des processus à temps continu, PhD thesis, Université Pierre et Marie Curie (Paris 6), 1994

[10] Fan, J. Design-adaptive nonparametric regression, J. Amer. Statist. Assoc., Volume 21 (1992), pp. 196-216

[11] Fan, J. Local linear regression smoothers and their minimax efficiency, Ann. Statist., Volume 21 (1993), pp. 196-216

[12] Fan, J.; Gijbels, I. Local Polynomial Modelling and Its Applications, Chapman & Hall, London, 1996

[13] Viano, M.C.; Deniau, C.; Oppenheim, G. Continuous-time fractional ARMA processes, Statist. Probab. Lett., Volume 21 (1994), pp. 323-336

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☆ Supported partly by Natural Science Foundation of China (Project Number: 70832005) and Shanghai Leading Academic Discipline Project, Project Number: B210.