Copula-based predictions in small area estimation

Abstract

Unit-level regression models are commonly used in small area estimation to obtain empirical best linear unbiased prediction of small area characteristics. A more flexible small area estimation model has been recently proposed using the linear regression to estimate the error terms and a multivariate exchangeable copula model to characterize the error distribution within each small area. In this work, 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. Further, we propose a bootstrap approach for both parametric and semi-parametric methods to obtain a nearly unbiased estimate of the mean squared prediction error (MSPE) of the EBUP of small area means. Performance of the proposed method is evaluated through a simulation study and also by a real data application.