  We consider a small area estimation model under square-root transformation in
the presence of functional measurement error. When measurement error is
present, the Bayes predictor can no longer be used as it depends on the
covariates even if parameters are known. Therefore suitable replacements are
called for, and we propose a predictor that only depends on observed responses
and data obtained from a large secondary survey. Moreover, some estimating
methods of unknown parameters are considered. In the simulations section, We
evaluate the performance using the mean squared prediction error (MSPE) and
discuss several scenarios in terms of the number of areas and the sample size
in a large secondary survey.
