  In the near future, millions of load curves measuring the electricity
consumption of French households in small time grids (probably half hours) will
be available. All these collected load curves represent a huge amount of
information which could be exploited using survey sampling techniques. In
particular, the total consumption of a specific cus- tomer group (for example
all the customers of an electricity supplier) could be estimated using unequal
probability random sampling methods. Unfortunately, data collection may undergo
technical problems resulting in missing values. In this paper we study a new
estimation method for the mean curve in the presence of missing values which
consists in extending kernel estimation techniques developed for longitudinal
data analysis to sampled curves. Three nonparametric estimators that take
account of the missing pieces of trajectories are suggested. We also study
pointwise variance estimators which are based on linearization techniques. The
particular but very important case of stratified sampling is then specifically
studied. Finally, we discuss some more practical aspects such as choosing the
bandwidth values for the kernel and estimating the probabilities of observation
of the trajectories.
