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: Local polynomial smoothing, -- derivative estimation, -- functional data, -- sampling density, -- plug-in bandwidth; Probabilities -- Periodicals; Mathematical statistics -- Periodicals; 519.2
• DOI: 10.1051/ps/2014009
• Languages: English
• ISSNs: 1292-8100

Abstract

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.