Local polynomial estimation of the mean function and its derivatives based on functional data and regular designs

Karim Benhenni; David Degras

ESAIM: Probability and Statistics (2014)

  • Volume: 18, page 881-899
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Benhenni, Karim, and Degras, David. "Local polynomial estimation of the mean function and its derivatives based on functional data and regular designs." ESAIM: Probability and Statistics 18 (2014): 881-899. <http://eudml.org/doc/273653>.

@article{Benhenni2014,
abstract = {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.},
author = {Benhenni, Karim, Degras, David},
journal = {ESAIM: Probability and Statistics},
keywords = {local polynomial smoothing; derivative estimation; functional data; sampling density; plug-in bandwidth},
language = {eng},
pages = {881-899},
publisher = {EDP-Sciences},
title = {Local polynomial estimation of the mean function and its derivatives based on functional data and regular designs},
url = {http://eudml.org/doc/273653},
volume = {18},
year = {2014},
}

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
PB - EDP-Sciences
VL - 18
SP - 881
EP - 899
AB - 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.
LA - eng
KW - local polynomial smoothing; derivative estimation; functional data; sampling density; plug-in bandwidth
UR - http://eudml.org/doc/273653
ER -

References

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