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For estimating area-specific parameters (quantities) in a finite population,a mixed model prediction approach is attractive. However, this approachstrongly depends on the normality assumption of the response values although weoften encounter a non-normal case in practice. In such a case, transformingobservations to make them suitable for normality assumption is a useful tool,but the problem of selecting suitable transformation still remains open. Toovercome the difficulty, we here propose a new empirical best predicting methodby using a parametric family of transformations to estimate a suitabletransformation based on the data. We suggest a simple estimating method fortransformation parameters based on the profile likelihood function, whichachieves consistency under some conditions on transformation functions. Formeasuring variability of point prediction, we construct an empirical Bayesconfidence interval of the population parameter of interest. Through simulationstudies, we investigate numerical performance of the proposed methods. Finally,we apply the proposed method to synthetic income data in Spanish provinces inwhich the resulting estimates indicate that the commonly usedlog-transformation would not be appropriate.

Adaptively Transformed Mixed Model Prediction of General Finite Population Parameters