2017/05/11 by Shonosuke Sugasawa, Sugasawa, Shonosuke, Tatsuya Kubokawa +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #Economic and Environmental Valuation #FOS: Computer and information sciences #Income, Poverty, and Inequality #Methodology (stat.ME) #demographic modeling and climate adaptation
paper · pdf · doi:10.48550/arxiv.1705.04136
openalex publication_date 2017/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For estimating area-specific parameters (quantities) in a finite population, a mixed model prediction approach is attractive. However, this approach strongly depends on the normality assumption of the response values although we often encounter a non-normal case in practice. In such a case, transforming observations to make them suitable for normality assumption is a useful tool, but the problem of selecting suitable transformation still remains open. To overcome the difficulty, we here propose a new empirical best predicting method by using a parametric family of transformations to estimate a suitable transformation based on the data. We suggest a simple estimating method for transformation parameters based on the profile likelihood function, which achieves consistency under some conditions on transformation functions. For measuring variability of point prediction, we construct an empirical Bayes confidence interval of the population parameter of interest. Through simulation studies, we investigate numerical performance of the proposed methods. Finally, we apply the proposed method to synthetic income data in Spanish provinces in which the resulting estimates indicate that the commonly used log-transformation would not be appropriate.