[L'optimalité et la suroptimalité du lissage localement linéaire de la fonction de régression]
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.
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@article{CRMATH_2010__348_3-4_211_0, author = {Shen, Jia and Sun, Shuguang}, title = {Optimal and superoptimal convergence rate of the local linear estimator of nonparametric regression function in continuous time}, journal = {Comptes Rendus. Math\'ematique}, pages = {211--215}, publisher = {Elsevier}, volume = {348}, number = {3-4}, year = {2010}, doi = {10.1016/j.crma.2009.12.005}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2009.12.005/} }
TY - JOUR AU - Shen, Jia AU - Sun, Shuguang TI - Optimal and superoptimal convergence rate of the local linear estimator of nonparametric regression function in continuous time JO - Comptes Rendus. Mathématique PY - 2010 SP - 211 EP - 215 VL - 348 IS - 3-4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2009.12.005/ DO - 10.1016/j.crma.2009.12.005 LA - en ID - CRMATH_2010__348_3-4_211_0 ER -
%0 Journal Article %A Shen, Jia %A Sun, Shuguang %T Optimal and superoptimal convergence rate of the local linear estimator of nonparametric regression function in continuous time %J Comptes Rendus. Mathématique %D 2010 %P 211-215 %V 348 %N 3-4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2009.12.005/ %R 10.1016/j.crma.2009.12.005 %G en %F CRMATH_2010__348_3-4_211_0
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://archive.numdam.org/articles/10.1016/j.crma.2009.12.005/
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