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

TL;DR

This paper develops robust estimation methods for total electricity consumption curves in finite populations, effectively handling outliers and skewness in the data, with practical evaluation on Irish electricity load data.

Contribution

It introduces new robust estimators based on conditional bias and functional methods for total curve estimation in the presence of outliers.

Findings

Robust estimators reduce sensitivity to outliers.

Mean square error estimators are derived for the new methods.

Performance evaluation on Irish data demonstrates effectiveness.

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.