Small area estimation with mixed models: a review
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Theory and Practice of Surveys
Small area estimation with mixed models: a review Shonosuke Sugasawa1 · Tatsuya Kubokawa2 Received: 22 December 2019 / Accepted: 19 March 2020 © Japanese Federation of Statistical Science Associations 2020
Abstract Small area estimation is recognized as an important tool for producing reliable esti‑ mates under limited sample information. This paper reviews techniques of small area estimation using mixed models, covering from basic to recently proposed advanced ones. We first introduce basic mixed models for small area estimation, and provide several methods for computing mean squared errors and confidence intervals which are important for measuring uncertainty of small area estimators. Then we provide reviews of recent development and techniques in small area estimation. This paper could be useful not only for researchers who are interested in details on the meth‑ odological research in small area estimation, but also for practitioners who might be interested in the application of the basic and new methods. Keywords Best linear unbiased predictor · Empirical Bayes · Fay–Herriot model · Hierarchical Bayes · Linear mixed model · Maximum likelihood estimator · Mean squared error · Nested error regression model · Shrinkage
1 Introduction The terms ‘small area’ or ‘small domain’ refers to a small geographical region such as a county, municipality or state, or a small demographic group such as a specific age–sex–race group. In the estimation of a characteristic of such a small group, the direct estimate based on only the data from the small group is likely to be unreliable, because only the small number of observations are available from the small group. The problem of small area estimation is how to produce a reliable estimate for the characteristic of the small group, and the small area estimation has been actively and extensively studied from both theoretical and practical aspects due to an increas‑ ing demand for reliable small area estimates from public and private sectors. The * Tatsuya Kubokawa [email protected]‑tokyo.ac.jp 1
Center for Spatial Information Science, The University of Tokyo, Tokyo, Japan
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Faculty of Economics, The University of Tokyo, 7‑3‑1 Hongo, Bunkyo‑ku, Tokyo 113‑0033, Japan
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Vol.:(0123456789)
Japanese Journal of Statistics and Data Science
articles Ghosh and Rao (1994) and Pfeffermann (2013) give good reviews and moti‑ vations, and the comprehensive book Rao and Molina (2015) covers all the main developments in small area estimation. Also see Demidenko (2004) for general mixed models and Pratesi (2016) for the analysis of poverty data by small area esti‑ mation. In this paper, we describe the details of classical methods and give a review of recent developments, which will be helpful for readers who are interested in this topic. To improve the accuracy of direct survey estimates, we make use of the relevant supplementary information such as data from other related areas and covariate data from other sources. The linear mixed models (LMM) enable us
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