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Biometrika Advance Access published online on November 4, 2008
Biometrika, doi:10.1093/biomet/asn048
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© 2008 Biometrika Trust

Article

Small area estimation when auxiliary information is measured with error

Lynn M. R. Ybarra

43210 West Oster Drive, Maricopa, Arizona 85238, U.S.A. lynnybarra{at}hotmail.com

Sharon L. Lohr

Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287-1804, U.S.A. sharon.lohr{at}asu.edu

Received for publication 1 January 2007. Revision received 1 May 2008.
  Abstract

Small area estimation methods typically combine direct estimates from a survey with predictions from a model in order to obtain estimates of population quantities with reduced mean squared error. When the auxiliary information used in the model is measured with error, using a small area estimator such as the Fay–Herriot estimator while ignoring measurement error may be worse than simply using the direct estimator. We propose a new small area estimator that accounts for sampling variability in the auxiliary information, and derive its properties, in particular showing that it is approximately unbiased. The estimator is applied to predict quantities measured in the U.S. National Health and Nutrition Examination Survey, with auxiliary information from the U.S. National Health Interview Survey.

Key Words: Best linear unbiased prediction • Domain estimation • Fay–Herriot model • Mean squared error estimation


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