@ARTICLE{10.21494/ISTE.OP.2021.0696, 

TITLE={Sur l’excès de la moyenne quadratique des erreurs associées à des fenêtres adaptatives dans l’estimation non-paramétrique de la tendance}, 
  
AUTHOR={Karim Benhenni, Didier A. Girard, Sana Louhichi, }, 
	
JOURNAL={Avancées en Mathématiques Pures et Appliquées}, 
	
VOLUME={12}, 

NUMBER={Numéro spécial : AUS-ICMS 2020}, 
	
YEAR={2021}, 

URL={https://openscience.fr/Sur-l-exces-de-la-moyenne-quadratique-des-erreurs-associees-a-des-fenetres}, 
	
DOI={10.21494/ISTE.OP.2021.0696}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={We consider the problem of the optimal selection of the smoothing parameter $$${h}$$$ in kernel estimation of a trend in nonparametric regression models with strictly stationary errors. We suppose that the errors are stochastic volatility sequences. Three types of volatility sequences are studied : the log-normal volatility, the Gamma volatility and the log-linear volatility with Bernoulli innovations. We take the weighted average squared error (ASE) as the global measure of performance of the trend estimation using $$${h}$$$ and we study two classical criteria for selecting $$${h}$$$ from the data, namely the adjusted generalized cross validation and Mallows-type criteria. We establish the asymptotic distribution of the gap between the ASE evaluated at one of these selectors and the smallest possible ASE. A Monte-Carlo simulation for a log-normal stochastic volatility model illustrates that this asymptotic approximation can be accurate even for small sample sizes.}}