  In this paper, we consider parametric transformed Fay-Herriot models, and
clarify conditions on transformations under which the estimator of the
transformation is consistent. It is shown that the dual power transformation
satisfies the conditions. Based on asymptotic properties for estimators of
parameters, we derive a second-order approximation of the prediction error of
the empirical best linear unbiased predictors (EBLUP) and obtain a second-order
unbiased estimator of the prediction error. Finally, performances of the
proposed procedures are investigated through simulation and empirical studies.
