The authors use an empirical Bayes (EB) approach to small area estimation under area-level unmatched sampling and linking models. Model parameters are estimated by a unified expectation and maximization (EM) algorithm and used to obtain EB estimators of area parameters. Results are extended to a nonparametric linking model based on a spline approximation. Approximate EB estimators that are computationally simpler are also obtained. Different bootstrap approaches to estimating the mean squared error (MSE) of the EB estimators are proposed. Results of a simulation study on the performance of the proposed methods are presented. Proposed methods are applied to data from a survey of family income and expenditure in Japan and poverty rates in Spanish provinces.

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Keywords Bootstrap, Empirical Bayes, Expectation–maximization algorithm, Fay–Herriot model, Mean squared error, Penalized spline
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Journal Test
Sugasawa, S. (Shonosuke), Kubokawa, T. (Tatsuya), & Rao, J.N.K. (2017). Small area estimation via unmatched sampling and linking models. Test, 1–21. doi:10.1007/s11749-017-0551-5