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).

中文翻译：

---

混合纵向研究的非参数协方差估计，在中年妇女健康中的应用

受混合纵向研究应用的启发，其中一组在不同年龄（横截面）进入研究的受试者连续多年（纵向）被跟踪，我们考虑使用噪声和部分观察到的功能轨迹样本进行非参数协方差估计。为了确保模型的可识别性和估计的一致性，我们引入并仔细讨论了降低秩和相邻不相干条件。所提出的算法基于顺序聚合方案，该方案是非迭代的，每个步骤中只有基本矩阵运算和封闭形式的解决方案。所提出方法的良好性能得到了理论和数值实验的支持。我们还根据女性研究的数据，将建议的程序应用于中年女性的工作记忆研究。