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.

Fay–Herriot model, Markov chain Monte Carlo, penalized spline, unmatched sampling and linking models
Scandinavian Journal of Statistics: Theory and App
School of Mathematics and Statistics

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