Estimation of eigenvalues, eigenvectors and scores in FDA models with dependent errors

Observations in functional data analysis (FDA) are often perturbed by random noise. In this paper we consider estimation of eigenvalues, eigenfunctions and scores for FDA models with weakly or strongly dependent error processes. As it turns out, the asymptotic distribution of estimated eigenvalues and eigenfunctions does not depend on the strength of dependence in the error process. In contrast, the rate of convergence and the asymptotic distribution of estimated scores differ distinctly between the cases of short and long memory. Simulations illustrate the asymptotic results.