LAUSR

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.