Small area estimation with multiple covariates under structural measurement error models

Abstract

Small area estimation is essential in making reliable inferences for areas where the sample is relatively small or no sample is available. In the case of developing a small area estimation model, if the covariates measured with errors were ignored, the estimation results may be worse than the direct estimate. Therefore, the problem of measurement error in covariates imposes challenges to data analytics in small area estimation. This paper studies a model with multiple covariates subject to structural measurement error and multiple error-free covariates. This study explores different scenarios in a simulation study by creating a finite super population spread across the area, investigating the sensitivity to sample size, and determining the variance of measurement error that was lower than the variance of the sampling error and the variance of the random effect. Jackknife method was employed to obtain a nearly unbiased estimator of the mean squared prediction error of empirical best predictors of the predictors of small area means. The research shows that the performance of the empirical best predictors is better in the case of a large sample size within the area and small variances of the measurement errors. The weighted version is recommended because it is more stable in terms of variability and bias.