Comptes Rendus
no. 8
Statistics
Non-parametric estimation of the average growth curve with a general non-stationary error process
[Estimation non paramétrique de la courbe de croissance pour un processus d'erreur non stationnaire]

Présenté par : Paul Deheuvels

Karim Benhenni1 ; Mustapha Rachdi1
1 Université de Grenoble, UFR SHS, BP 47, 38040 Grenoble cedex 09, France
Comptes Rendus. Mathématique, Volume 343 (2006) no. 8, pp. 541-544.

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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DOI : 10.1016/j.crma.2006.09.009
Karim Benhenni 1 ; Mustapha Rachdi 1

1 Université de Grenoble, UFR SHS, BP 47, 38040 Grenoble cedex 09, France 
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Karim Benhenni; Mustapha Rachdi. Non-parametric estimation of the average growth curve with a general non-stationary error process. Comptes Rendus. Mathématique, Volume 343 (2006) no. 8, pp. 541-544. doi : 10.1016/j.crma.2006.09.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.09.009/

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