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RESEARCH PRODUCT

Using Complex Surveys to Estimate theL1-Median of a Functional Variable: Application to Electricity Load Curves

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description

Mean proles are widely used as indicators of the electricity consumption habits of customers. Currently, Electricit e De France (EDF), estimates class load proles by using point-wise mean function. Unfortunately, it is well known that the mean is highly sensitive to the presence of outliers, such as one or more consumers with unusually high-levels of consumption. In this paper, we propose an alternative to the mean prole: the L1-median prole which is more robust. When dealing with large datasets of functional data (load curves for example), survey sampling approaches are useful for estimating the median prole and avoid storing all of the data. We propose here estimators of the median trajectory using several sampling strategies and estimators. A comparison between them is illustrated by means of a test population. We develop a stratication based on the linearized variable which substantially improves the accuracy of the estimator compared to simple random sampling without replacement. We suggest also an improved estimator that takes into account auxiliary information. Some potential areas for future research are also highlighted.