Adaptively transformed mixed-model prediction of general finite-population parameters

Shonosuke Sugasawa, Tatsuya Kubokawa

Research output: Contribution to journalArticlepeer-review


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 a 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 the variability of point prediction, we construct an empirical Bayes confidence interval of the population parameter of interest. Through simulation studies, we investigate the 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.

Original languageEnglish
Pages (from-to)1025-1046
Number of pages22
JournalScandinavian Journal of Statistics
Issue number4
Publication statusPublished - 2019 Dec 1
Externally publishedYes


  • confidence interval
  • empirical Bayes
  • finite population
  • mean squared error
  • random effect
  • small area estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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