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

ESAIM: Probability and Statistics (2014)

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

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topBenhenni, 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 -

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