Estimating the covariance function with functional data.

This paper describes a two-step procedure for estimating the covariance function and its eigenvalues and eigenfunctions in situations where the data are curves or functions. The first step produces initial estimates of eigenfunctions using a standard principal components analysis. At the second step, these initial estimates are smoothed via local polynomial fitting, with the bandwidth in the kernel function being selected by a data-driven procedure. The results of a simulation study and three real examples are presented to illustrate the performance of the proposed methodology.