Small area estimation using survey weights under a nested error linear regression model with structural measurement error

Previously, the nested error linear regression models using survey weights have been studied in small area estimation to obtain efficient model-based and design-consistent estimators of small area means. In particular, the pseudo-empirical Bayes (PEB) using survey weights has received a lot of attention and is being used in statistical agencies. The covariates in these nested error linear regression models are not subject to measurement errors. However, there are many situations that the covariates are subject to measurement errors. In this paper, we develop a nested error linear regression model with an area-level covariate subject to structural measurement error. In particular, we propose a PEB estimator to estimate small area means. This estimator borrows strength across areas through the model and makes use of the survey weights to preserve the design consistency as the area sample size increases. We also employ a parametric bootstrap approach to estimate the mean squared prediction error (MSPE) of the PEB predictor. Finally, we report the results of a simulation study on the performance of our PEB predictor and associated bootstrap MSPE estimator.