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.
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://archive.numdam.org/articles/10.1051/ps/2014009/} }
TY - JOUR AU - Benhenni, Karim AU - Degras, David TI - Local polynomial estimation of the mean function and its derivatives based on functional data and regular designs JO - ESAIM: Probability and Statistics PY - 2014 SP - 881 EP - 899 VL - 18 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2014009/ DO - 10.1051/ps/2014009 LA - en ID - PS_2014__18__881_0 ER -
%0 Journal Article %A Benhenni, Karim %A Degras, David %T Local polynomial estimation of the mean function and its derivatives based on functional data and regular designs %J ESAIM: Probability and Statistics %D 2014 %P 881-899 %V 18 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2014009/ %R 10.1051/ps/2014009 %G en %F PS_2014__18__881_0
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://archive.numdam.org/articles/10.1051/ps/2014009/
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