Sample-based estimation of mean electricity consumption curves for small domains

Many studies conducted by various electric utilities around the world are based on the analysis of mean electricity consumption curves for various subpopulations, particularly geographic in nature. Those mean curves are estimated from samples of thousands of curves measured at very short intervals over long periods. Estimation for small subpopulations, also called small domains, is a very timely topic in sampling theory. In this article, we will examine this problem based on functional data and we will try to estimate the mean curves for small domains. For this, we propose four methods: functional linear regression; modelling the scores of a principal component analysis by unit-level linear mixed models; and two non-parametric estimators, with one based on regression trees and the other on random forests, adapted to the curves. All these methods have been tested and compared using real electricity consumption data for households in France.