Non-Parametric Estimation for Aggregated Functional Data for Electric Load Monitoring

In this work we address the problem of estimating mean and covariance curves when the available sample consists on aggregated functional data. Consider a population divided into sub-populations for which one wants to estimate the mean (typology) and covariance curves for each sub-population. However, it is not possible (or too expensive) to obtain sample curves for single individuals. The available data are collective curves, sum of curves of different subsets of individuals belonging to the sub-populations. We propose an estimation method based on B-splines expansion. This method is consistent and simulation studies suggest that the proposed mean estimator is suitable even with very few replications. This problem was motivated by a real problem concerning the efficient distribution of electric energy in Southeast Brazil.