Parametric transformed Fay–Herriot model for small area estimation

Motivated from analysis of positive data such as income, revenue, harvests and production, the paper suggests the parametric transformed Fay–Herriot model in small-area estimation. When the dual power transformation is used as the parametric transformation, we provide consistent estimators of the transformation parameter, the regression coefficients and the variance component. The empirical best linear unbiased predictors which plug in those consistent estimators are suggested, and their mean squared errors (MSE) are asymptotically evaluated. A second-order unbiased estimator of the MSE is also given through the parametric bootstrap. Finally, performances of the suggested procedures are investigated through simulation and empirical studies.