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A BLUP Synthetic Versus an EBLUP Estimator: An Empirical Study of a Small Area Estimation Problem

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  • A. F. Militino
  • M. D. Ugarte
  • T. Goicoa

Abstract

Model-based estimators are becoming very popular in statistical offices because Governments require accurate estimates for small domains that were not planned when the study was designed, as their inclusion would have produced an increase in the cost of the study. The sample sizes in these domains are very small or even zero; consequently, traditional direct design-based estimators lead to unacceptably large standard errors. In this regard, model-based estimators that 'borrow information' from related areas by using auxiliary information are appropriate. This paper reviews, under the model-based approach, a BLUP synthetic and an EBLUP estimator. The goal is to obtain estimators of domain totals when there are several domains with very small sample sizes or without sampled units. We also provide detailed expressions of the mean squared error at different levels of aggregation. The results are illustrated with real data from the Basque Country Business Survey.

Suggested Citation

  • A. F. Militino & M. D. Ugarte & T. Goicoa, 2007. "A BLUP Synthetic Versus an EBLUP Estimator: An Empirical Study of a Small Area Estimation Problem," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(2), pages 153-165.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:2:p:153-165
    DOI: 10.1080/02664760600994893
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    References listed on IDEAS

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    1. Stukel, D. M. & Rao, J. N. K., 1997. "Estimation of regression models with nested error structure and unequal error variances under two and three stage cluster sampling," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 401-407, November.
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    Cited by:

    1. M. D. Ugarte & A. F. Militino & T. Goicoa, 2008. "Adjusting economic estimates in business surveys," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(11), pages 1253-1265.
    2. Militino, A.F. & Goicoa, T. & Ugarte, M.D., 2012. "Estimating the percentage of food expenditure in small areas using bias-corrected P-spline based estimators," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2934-2948.
    3. M. Ugarte & A. Militino & T. Goicoa, 2009. "Benchmarked estimates in small areas using linear mixed models with restrictions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 342-364, August.

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