n 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 positive/negative 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.

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• Constrained Bayes estimation in small area models with functional measurement error