Functional calibration estimation by the maximum entropy on the mean principle

TL;DR

This paper introduces a novel functional calibration estimation method in survey sampling using the maximum entropy on the mean principle, enhancing accuracy over traditional estimators by incorporating auxiliary information within a functional data framework.

Contribution

It extends calibration estimation to functional data using the maximum entropy on the mean principle, providing a new approach for estimating population means with improved accuracy.

Findings

Functional calibration estimator outperforms Horvitz-Thompson estimator in simulations.

The method incorporates Gaussian and Poisson prior measures.

The approach is grounded in an infinite dimensional linear inverse problem.

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 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.