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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