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For marketing or power grid management purposes, many studies based on theanalysis of the total electricity consumption curves of groups of customers arenow carried out by electricity companies. Aggregated total or mean load curvesare estimated using individual curves measured at fine time grid and collectedaccording to some sampling design. Due to the skewness of the distribution ofelectricity consumptions, these samples often contain outlying curves which mayhave an important impact on the usual estimation procedures. We introduceseveral robust estimators of the total consumption curve which are notsensitive to such outlying curves. These estimators are based on theconditional bias approach and robust functional methods. We also derive meansquare error estimators of these robust estimators and finally, we evaluate andcompare the performance of the suggested estimators on Irish electricity data.

Conditional bias robust estimation of the total of curve data by sampling in a finite population: an illustration on electricity load curves