Local polynomial estimation of the mean function and its derivatives based on functional data and regular designs
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 independent realizations of the process are observed at a sampling design of size generated by a positive density, we derive the asymptotic bias and variance of the local polynomial estimator as increase to infinity. We deduce optimal sampling densities, optimal bandwidths,...