Title: Nonparametric covariance estimation for mixed longitudinal studies, with applications in midlife women's health,
Abstract: Motivated by applications of mixed longitudinal studies, where a group of
subjects entering the study at different ages (cross-sectional) are followed
for successive years (longitudinal), we consider nonparametric covariance
estimation with samples of noisy and partially-observed functional
trajectories. To ensure model identifiability and estimation consistency, we
introduce and carefully discuss the reduced rank and neighboring incoherence
condition. The proposed algorithm is based on a sequential-aggregation scheme,
which is non-iterative, 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 midlife women's working memory study based on the data from the
Study of Women's Health Across the Nation (SWAN).