Title: Conditional bias robust estimation of the total of curve data by sampling in a finite population: an illustration on electricity load curves,
Abstract: For marketing or power grid management purposes, many studies based on the
analysis of the total electricity consumption curves of groups of customers are
now carried out by electricity companies. Aggregated total or mean load curves
are estimated using individual curves measured at fine time grid and collected
according to some sampling design. Due to the skewness of the distribution of
electricity consumptions, these samples often contain outlying curves which may
have an important impact on the usual estimation procedures. We introduce
several robust estimators of the total consumption curve which are not
sensitive to such outlying curves. These estimators are based on the
conditional bias approach and robust functional methods. We also derive mean
square error estimators of these robust estimators and finally, we evaluate and
compare the performance of the suggested estimators on Irish electricity data.