Semiparametric Models with Functional Responses in a Model Assisted Survey Sampling Setting : Model Assisted Estimation of Electricity Consumption Curves

摘要

This work adopts a survey sampling point of view to estimate the mean curve of large databases of functional data. When storage capacities are limited, selecting, with survey techniques a small fraction of the observations is an interesting alternative to signal compression techniques. We propose here to take account of real or multivariate auxiliary information available at a low cost for the whole population, with semiparametric model assisted approaches, in order to improve the accuracy of Horvitz-Thompson estimators of the mean curve. We first estimate the functional principal components with a design based point of view in order to reduce the dimension of the signals and then propose semiparametric models to get estimations of the curves that are not observed. This technique is shown to be really effective on a real dataset of 18902 electricity meters measuring every half an hour electricity consumption during two weeks.