Area-level unmatched sampling and linking models have been widely used as a model-based method for producing reliable estimates of small-area means. However, one practical difficulty is the specification of a link function. In this paper, we relax the assumption of a known link function by not specifying its form and estimating it from the data. A penalized-spline method is adopted for estimating the link function, and a hierarchical Bayes method of estimating area means is developed using a Markov chain Monte Carlo method for posterior computations. Results of simulation studies comparing the proposed method with a conventional approach based on a known link function are presented. In addition, the proposed method is applied to data from the Survey of Family Income and Expenditure in Japan and poverty rates in Spanish provinces.

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Keywords Fay–Herriot model, Markov chain Monte Carlo, penalized spline, unmatched sampling and linking models
Persistent URL dx.doi.org/10.1111/sjos.12376
Journal Scandinavian Journal of Statistics: Theory and App
Citation
Sugasawa, S. (Shonosuke), Kubokawa, T. (Tatsuya), & Rao, J.N.K. (2018). Hierarchical Bayes small-area estimation with an unknown link function. Scandinavian Journal of Statistics: Theory and App. doi:10.1111/sjos.12376