We extend the problem of obtaining an estimator for the finite populationmean parameter incorporating complete auxiliary information through calibrationestimation in survey sampling but considering a functional data framework. Thefunctional calibration sampling weights of the estimator are obtained bymatching the calibration estimation problem with the maximum entropy on themean principle. In particular, the calibration estimation is viewed as aninfinite dimensional linear inverse problem following the structure of themaximum entropy on the mean approach. We give a precise theoretical setting andestimate the functional calibration weights assuming, as prior measures, thecentered Gaussian and compound Poisson random measures. Additionally, through asimple simulation study, we show that our functional calibration estimatorimproves its accuracy compared with the Horvitz-Thompson estimator.
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