Estimating the RMSE of Small Area Estimates without the Tears

Diane Hindmarsh and David Steel
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Diane Hindmarsh: National Institute for Applied Statistics Research Australia, School of Mathematics and Applied Statistics, Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong, NSW 2252, Australia
David Steel: National Institute for Applied Statistics Research Australia, School of Mathematics and Applied Statistics, Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong, NSW 2252, Australia

Stats, 2021, vol. 4, issue 4, 1-12

Abstract: Small area estimation (SAE) methods can provide information that conventional direct survey estimation methods cannot. The use of small area estimates based on linear and generalized linear mixed models is still very limited, possibly because of the perceived complexity of estimating the root mean square errors (RMSEs) of the estimates. This paper outlines a study used to determine the conditions under which the estimated RMSEs, produced as part of statistical output (‘plug-in’ estimates of RMSEs) could be considered appropriate for a practical application of SAE methods where one of the main requirements was to use SAS software. We first show that the estimated RMSEs created using an EBLUP model in SAS and those obtained using a parametric bootstrap are similar to the published estimated RMSEs for the corn data in the seminal paper by Battese, Harter and Fuller. We then compare plug-in estimates of RMSEs from SAS procedures used to create EBLUP and EBP estimators against estimates of RMSEs obtained from a parametric bootstrap. For this comparison we created estimates of current smoking in males for 153 local government areas (LGAs) using data from the NSW Population Health Survey in Australia. Demographic variables from the survey data were included as covariates, with LGA-level population proportions, obtained mainly from the Australian Census used for prediction. For the EBLUP, the estimated plug-in estimates of RMSEs can be used, provided the sample size for the small area is more than seven. For the EBP, the plug-in estimates of RMSEs are suitable for all in-sample areas; out-of-sample areas need to use estimated RMSEs that use the parametric bootstrap.

Keywords: small area estimation; SAE; empirical best predictor; MSE; parametric bootstrap; model-based survey estimation; SAS procedures (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2021
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