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 : 10.1051/ps/2014009
Classification : 62G08, 62G20
Keywords: local polynomial smoothing, derivative estimation, functional data, sampling density, plug-in bandwidth 
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     title = {Local polynomial estimation of the mean function and its derivatives based on functional data and regular designs},
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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

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