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Title: Estimation of mean electricity consumption curves for small areas Authors:  Anne de Moliner - Universite de Bourgogne EDF (France) [presenting]
Herve Cardot - Universite de Bourgogne (France)
Camelia Goga - Universite de Bourgogne (France)
Abstract: The French electricity company EDF is interested in estimating the mean electricity consumption curves of different groups of customers for marketing purposes. These aggregated electricity consumption curves are estimated using samples of thousands of curves selected according to a sampling design and measured at a small time step. Today, there is a growing need for estimations not only at the national level but also for small geographic regions. For some of these regions, there are few units in our panels so the estimators can be very imprecise. This problem of small area estimation in a finite population is very usual in survey sampling and is often addressed by borrowing strength among areas through an explicit modelling of the relation between the auxiliary information and the variable of interest. The goal will be to adapt this existing methodology, developed for totals of real variables, to the framework of functional data. To that purpose two methods are proposed: the first one consists in using a functional principal components analysis in order to transform our functional problem into several uncorrelated real total estimation problems that we can address using standard linear mixed models (known in survey sampling as Unit Level Models). The other method consists in predicting the curve of each non sampled unit using regression trees or random forests adapted to functional data. These methods are tested on real datasets and compared to each other.