Small area estimation with multiple covariates measured with errors: A nested error linear regression approach of combining multiple surveys

Abstract

Small area estimation has become a very active area of research in statistics. Many models studied in small area estimation focus on one or more variables of interest from a single survey without paying close attention to the nature of the covariates. It is useful to utilize the idea of borrowing strength from covariates to build a model which combines two (or multiple) surveys. In many real applications, there are also covariates measured with errors. In this paper, we study a nested error linear regression model which has multiple unit- or area-level error-free covariates, possibly coming from administrative records, and multiple area-level covariates subject to structural measurement error where the data on the latter covariates are obtained from multiple surveys. In particular, we derive empirical best predictors of small area means and estimators of mean squared prediction error of the empirical best predictors of small area means. Performance of the proposed approach is studied through a simulation study and also by a real application.