  We extend the problem of obtaining an estimator for the finite population
mean parameter incorporating complete auxiliary information through calibration
estimation in survey sampling but considering a functional data framework. The
functional calibration sampling weights of the estimator are obtained by
matching the calibration estimation problem with the maximum entropy on the
mean principle. In particular, the calibration estimation is viewed as an
infinite dimensional linear inverse problem following the structure of the
maximum entropy on the mean approach. We give a precise theoretical setting and
estimate the functional calibration weights assuming, as prior measures, the
centered Gaussian and compound Poisson random measures. Additionally, through a
simple simulation study, we show that our functional calibration estimator
improves its accuracy compared with the Horvitz-Thompson estimator.
