Local polynomial estimation of the mean function and its derivatives based on functional data and regular designs
ESAIM: Probability and Statistics, Tome 18 (2014) , pp. 881-899.

We study the estimation of the mean function of a continuous-time stochastic process and its derivatives. The covariance function of the process is assumed to be nonparametric and to satisfy mild smoothness conditions. Assuming that n independent realizations of the process are observed at a sampling design of size N generated by a positive density, we derive the asymptotic bias and variance of the local polynomial estimator as n,N increase to infinity. We deduce optimal sampling densities, optimal bandwidths, and propose a new plug-in bandwidth selection method. We establish the asymptotic performance of the plug-in bandwidth estimator and we compare, in a simulation study, its performance for finite sizes n,N to the cross-validation and the optimal bandwidths. A software implementation of the plug-in method is available in the R environment.

DOI : https://doi.org/10.1051/ps/2014009
Classification : 62G08,  62G20
Mots clés : local polynomial smoothing, derivative estimation, functional data, sampling density, plug-in bandwidth
@article{PS_2014__18__881_0,
author = {Benhenni, Karim and Degras, David},
title = {Local polynomial estimation of the mean function and its derivatives based on functional data and regular designs},
journal = {ESAIM: Probability and Statistics},
pages = {881--899},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2014009},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2014009/}
}
Benhenni, Karim; Degras, David. Local polynomial estimation of the mean function and its derivatives based on functional data and regular designs. ESAIM: Probability and Statistics, Tome 18 (2014) , pp. 881-899. doi : 10.1051/ps/2014009. http://www.numdam.org/articles/10.1051/ps/2014009/

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