Copula‐based predictions in small area estimation

Abstract

Unit-level regression models are commonly used in small area estimation (SAE) to obtain an empirical best linear unbiased prediction of small area characteristics. The underlying assumptions of these models, however, may be unrealistic in some applications. Previous work developed a copula-based SAE model where the empirical Kendall's tau was used to estimate the dependence between two units from the same area. In this article, we propose a likelihood framework to estimate the intra-class dependence of the multivariate exchangeable copula for the empirical best unbiased prediction (EBUP) of small area means. One appeal of the proposed approach lies in its accommodation of both parametric and semi-parametric estimation approaches. Under each estimation method, we further propose a bootstrap approach to obtain a nearly unbiased estimator of the mean squared prediction error of the EBUP of small area means. The performance of the proposed methods is evaluated through simulation studies and also by a real data application.

Copula-Based Prediction of Small Area Estimation for Youth Mean Years of Schooling in West Java Province

“…The application of small-area estimation based on sample data has the problem of being unable to determine the actual parameter values. The bootstrap approach can overcome the estimated MSPE [3], so the mean squared error value is calculated using the following formula…”