Functional data approaches for mixed longitudinal studies, with applications in midlife women's health
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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 novel 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).
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