[Estimation non paramétrique de la courbe de croissance pour un processus d'erreur non stationnaire]
L'estimation non paramétrique de la courbe de croissance moyenne pour des données répétées et avec un processus d'erreur non stationnaire a été étudiée, pour des formes particulières de la fonction d'autocovariance, par plusieurs auteurs. Pour ce même problème, nous avons étudié l'estimation de la fonction de croissance avec un processus d'erreur non stationnaire généralisé (pas de forme spécifique de sa fonction d'autocovariance). La fenêtre optimale obtenue dépend de la singularité de la fonction d'autocovariance sur la diagonale.
The non-parametric estimation of the average growth curve has been extensively studied in both stationary and some non-stationary particular situations. In this Note, we consider the statistical problem of estimating the average growth curve for a fixed design model with a non-stationary error process. The non-stationarity considered here is of a general form, and this note may be considered as an extension of previous results. The optimal bandwidth is shown to depend on the singularity of the autocovariance function of the error process along the diagonal.
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@article{CRMATH_2006__343_8_541_0,
author = {Benhenni, Karim and Rachdi, Mustapha},
title = {Non-parametric estimation of the average growth curve with a general non-stationary error process},
journal = {Comptes Rendus. Math\'ematique},
pages = {541--544},
publisher = {Elsevier},
volume = {343},
number = {8},
year = {2006},
doi = {10.1016/j.crma.2006.09.009},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.09.009/}
}
TY - JOUR AU - Benhenni, Karim AU - Rachdi, Mustapha TI - Non-parametric estimation of the average growth curve with a general non-stationary error process JO - Comptes Rendus. Mathématique PY - 2006 SP - 541 EP - 544 VL - 343 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.09.009/ DO - 10.1016/j.crma.2006.09.009 LA - en ID - CRMATH_2006__343_8_541_0 ER -
%0 Journal Article %A Benhenni, Karim %A Rachdi, Mustapha %T Non-parametric estimation of the average growth curve with a general non-stationary error process %J Comptes Rendus. Mathématique %D 2006 %P 541-544 %V 343 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.09.009/ %R 10.1016/j.crma.2006.09.009 %G en %F CRMATH_2006__343_8_541_0
Benhenni, Karim; Rachdi, Mustapha. Non-parametric estimation of the average growth curve with a general non-stationary error process. Comptes Rendus. Mathématique, Tome 343 (2006) no. 8, pp. 541-544. doi : 10.1016/j.crma.2006.09.009. http://www.numdam.org/articles/10.1016/j.crma.2006.09.009/
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