Functional calibration estimation by the maximum entropy on the mean principle |
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Authors: | S Gallón F Gamboa JM Loubes |
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Institution: | 1. Departamento de Matemáticas y Estadística, Facultad de Ciencias Económicas, Universidad de Antioquia, Medellín, Colombia;2. Institut de Mathématiques de Toulouse, Université Toulouse III Paul Sabatier, Toulouse, Francesantiagog@udea.edu.co;4. Institut de Mathématiques de Toulouse, Université Toulouse III Paul Sabatier, Toulouse, France |
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Abstract: | We extend the problem of obtaining an estimator for the finite population mean parameter incorporating complete auxiliary information through calibration estimation in survey sampling under 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 – MEM – principle. In particular, the calibration estimation is viewed as an infinite-dimensional linear inverse problem following the structure of the MEM approach. We give a precise theoretical setting and estimate the functional calibration weights assuming, as prior measures, the centred Gaussian and compound Poisson random measures. Additionally, through a simple simulation study, we show that the proposed functional calibration estimator improves its accuracy compared with the Horvitz–Thompson one. |
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Keywords: | auxiliary information functional calibration weights functional data infinite-dimensional linear inverse problems survey sampling |
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