@ARTICLE{10.21494/ISTE.OP.2021.0696, 

TITLE={On the excess of average squared error for data-driven bandwidths in nonparametric trend estimation}, 
  
AUTHOR={Karim Benhenni, Didier A. Girard, Sana Louhichi, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={12}, 

NUMBER={Issue 3 (Special AUS-ICMS 2020)}, 
	
YEAR={2021}, 

URL={https://openscience.fr/On-the-excess-of-average-squared-error-for-data-driven-bandwidths-in}, 
	
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.}}