Functional calibration estimation by the maximum entropy on the mean principle

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.

Comments on: Deville and Särndal’s calibration: revisiting a 25 years old successful optimization problem

“…In this respect, [6] proposed a Horvitz Thompson estimator of the mean trajectory, and under certain assumptions regarding the sampling design, a functional central limit theorem has been proposed. Based on this estimator, [8] extended the approach taken to obtaining calibration sampling weights using functional data.…”

Quality-Achieving Reliability Assessment of Rolling Bearing Based on Bootstrap Maximum Entropy Method and Similarity Method

“…Therefore, PDF of the bearing quality-influencing factors and the bearing vibration acceleration are established by BMEM which is a novel method that combines the advantages of the bootstrap method 27 and the maximum entropy method. 28 , 29 The similarity method is used to obtain the weight of bearing quality-influencing factors by calculating the similarity between the PDF of the bearing quality-influencing factors and the PDF of the bearing vibration acceleration. The weight refers to the degree of overlap between the probability density curve of the vibration acceleration and the probability density curve of the quality-influencing factor, as shown in Figure 1 .…”

A Relationship between the Ordinary Maximum Entropy Method and the Method of Maximum Entropy in the Mean

“…For what comes below, and to relate to the first problem, we shall restrict ourselves to the convex set of continuous density functions. Such type of problems were considered for example in [9] or in much grater generality in [10] or and more recently in [11] where applications and further references to related work are collected. As mentioned above, the setup can be relaxed considerable at the expense of technicalities.…”