Abstract: In mixed longitudinal studies, a group of subjects enter the study at different ages (cross-sectional) and are followed for successive years (longitudinal). In the context of such studies, we consider nonparametric covariance estimation with samples of noisy and partially observed functional trajectories. The proposed algorithm is based on a noniterative sequential-aggregation scheme with only basic matrix operations and closed-form solutions in each step. The good performance of the proposed method is supported by both theory and numerical experiments. We also apply the proposed procedure to a study on the working memory of midlife women, based on data from the Study of Women's Health Across the Nation (SWAN).

Key words and phrases: Consistency, covariance estimation, cross-sectional, functional data, longitudinal studies, partial trajectories.