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Benchmarking Small Area Estimators

William R. Bell, Gauri S. Datta, and Malay Ghosh


Augmented model; Best linear unbiased; External; Internal; Optimal; Orthogonal projection


This paper considers benchmarking issues in the context of small area estimation. We find optimal estimators within the class of benchmarked linear estimators under either external or internal benchmark constraints. This extends existing results for both external and internal benchmarking, and also provides some links between the two. In addition, necessary and sufficient conditions for self-benchmarking are found for an augmented model. Most results of this paper are found using ideas of orthogonal projection.


William R. Bell, Gauri S. Datta, and Malay Ghosh. (2012). Benchmarking Small Area Estimators. Center for Statistical Research & Methodology Research Report Series (Statistics #2012-12). U.S. Census Bureau. Available online at <>.

Source: U.S. Census Bureau, Center for Statistical Research & Methodology, Research and Methodology Directorate

Published online: September 12, 2012
Last revised: September 12, 2012


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Source: U.S. Census Bureau | Research and Methodology Directorate | Center for Statistical Research & Methodology | (301) 763-3215 (or |   Last Revised: September 11, 2013