Constrained Bayes estimation in small area models with functional measurement error

摘要

In survey sampling, policy decisions regarding allocation of resources to subgroups, called small areas, or determination of subgroups with specific properties in a population are based on reliable estimates of small area parameters. However, the information is often collected at a different scale than these subgroups. Hence, we need to estimate characteristics of subgroups based on the coarser scale data. One of the main interests in small area estimation is to produce an ensemble of small area parameters whose distribution across small areas is close to the corresponding distribution of true parameters. In this paper, we consider the unit-level nested error linear regression model which is commonly used in small area estimation. We study the case where the covariate in the model is assumed to have measurement error. To study this complex model, we propose to use constrained Bayes method to estimate the true covariate to build the small area Bayes predictor. We also provide some measures of performance such as sensitivity, specificity, and positiveegative predictive values for the constructed Bayes predictor. We estimate the model parameters using the method of moments and Bayesian approach to get corresponding empirical and hierarchical Bayes predictors. The performance of our proposed approach is evaluated through a simulation study and a real data application.