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In the near future, millions of load curves measuring the electricityconsumption of French households in small time grids (probably half hours) willbe available. All these collected load curves represent a huge amount ofinformation which could be exploited using survey sampling techniques. Inparticular, the total consumption of a specific cus- tomer group (for exampleall the customers of an electricity supplier) could be estimated using unequalprobability random sampling methods. Unfortunately, data collection may undergotechnical problems resulting in missing values. In this paper we study a newestimation method for the mean curve in the presence of missing values whichconsists in extending kernel estimation techniques developed for longitudinaldata analysis to sampled curves. Three nonparametric estimators that takeaccount of the missing pieces of trajectories are suggested. We also studypointwise variance estimators which are based on linearization techniques. Theparticular but very important case of stratified sampling is then specificallystudied. Finally, we discuss some more practical aspects such as choosing thebandwidth values for the kernel and estimating the probabilities of observationof the trajectories.

Estimating with kernel smoothers the mean of functional data in a finite  population setting. A note on variance estimation in presence of partially  observed trajectories