Derivative estimation of the mean of longitudinal and functional data is useful, because it provides a quantitative measure of changes in the mean function that can be used for modeling of the data. We propose a general method for estimation of the derivative of the mean function that allows us to make inference about both longitudinal and functional data regardless of the sparsity of data. The $$L^2$$ L 2 and uniform convergence rates of the local linear estimator for the true derivative of the mean function are derived. Then the optimal weighting scheme under the $$L^2$$ L 2 rate of convergence is obtained. The performance of the proposed method is evaluated by a simulation study, and additionally compared with another existing method. The method is used to analyse a real data set involving children weight growth failure.

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关于纵向和功能数据的平均导数估计：从稀疏到密集

纵向和功能数据的均值的导数估计很有用，因为它提供了可用于数据建模的均值函数变化的定量测量。我们提出了一种估计均值函数导数的通用方法，该方法使我们能够对纵向和功能数据进行推断，而不管数据的稀疏性如何。推导出均值函数的真导数的$$L^2$$L 2 和局部线性估计器的均匀收敛率。然后得到$$L^2$$L 2 收敛率下的最优加权方案。通过仿真研究评估了所提出方法的性能，并与另一种现有方法进行了比较。该方法用于分析涉及儿童体重增长失败的真实数据集。