Local polynomial estimation of the mean function and its derivatives based on functional data and regular designs. (29th October 2014)

• Record Type: Journal Article
• Authors: Benhenni, Karim; Degras, David
• Is Part Of: ESAIM. Volume 18(2014)
• Page Start: 881
• Page End: 899
• Publication Date: 2014-10-29
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; 519.2
• DOI: 10.1051/ps/2014009
• Languages: English
• ISSNs: 1292-8100

Abstract

<abstract abstract-type="normal" xml:lang="en"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>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 <italic>n</italic> independent realizations of the process are observed at a sampling design of size <italic>N</italic> generated by a positive density, we derive the asymptotic bias and variance of the local polynomial estimator as <italic>n, N</italic> 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 <italic>n, N</italic> to the cross-validation and the optimal bandwidths. A software implementation of the plug-in method is available in the R environment.</p> </abstract>