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Benchmarked Estimators for a Small Area Mean Under a Onefold Nested Regression Model

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  • Marius Stefan
  • Michael Hidiroglou

Abstract

In this paper, we modify small area estimators, based on the unit‐level model, so that they add up to reliable higher‐level estimates of population totals. These modifications result in benchmarked small area estimators. We consider two benchmarking procedures. One is based on augmenting the unit‐level model with a suitable variable. The other one uses the calibrated weights of the direct estimators that are reliable at the higher levels. These weights are used in estimators that are based on the aggregation of the unit‐level model for each small area. The mean squared error estimators of the proposed benchmarked estimators are obtained by suitably modifying those associated with the corresponding non benchmarked estimators. The properties of the estimators are evaluated via simulation.

Suggested Citation

  • Marius Stefan & Michael Hidiroglou, 2021. "Benchmarked Estimators for a Small Area Mean Under a Onefold Nested Regression Model," International Statistical Review, International Statistical Institute, vol. 89(1), pages 108-131, April.
    • Handle: RePEc:bla:istatr:v:89:y:2021:i:1:p:108-131
    DOI: 10.1111/insr.12380
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    References listed on IDEAS

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    1. G. Datta & M. Ghosh & R. Steorts & J. Maples, 2011. "Bayesian benchmarking with applications to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 574-588, November.
    2. Malay Ghosh & Rebecca Steorts, 2013. "Two-stage benchmarking as applied to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 670-687, November.
    3. Pfeffermann, Danny & Sverchkov, Michail, 2007. "Small-Area Estimation Under Informative Probability Sampling of Areas and Within the Selected Areas," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1427-1439, December.
    4. W. R. Bell & G. S. Datta & M. Ghosh, 2013. "Benchmarking small area estimators," Biometrika, Biometrika Trust, vol. 100(1), pages 189-202.
    5. Pfeffermann, Danny & Barnard, Charles H, 1991. "Some New Estimators for Small-Area Means with Application to the Assessment of Farmland Values," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 73-84, January.
    6. Pfeffermann, Danny & Tiller, Richard, 2006. "Small-Area Estimation With StateSpace Models Subject to Benchmark Constraints," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1387-1397, December.
    7. 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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