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Small area estimation of general parameters under complex sampling designs

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  • Rao, J.N.K.
  • Molina, Isabel
  • Guadarrama, María

Abstract

When the probabilities of selecting the individuals for the sample depend on the outcome values, we say that the selection mechanism is informative. Under informative selection, individuals with certain outcome values appear more often in the sample and therefore the sample is not representative of the population. As a consequence, usual model-based inference based on the actual sample without appropriate weighting might be strongly biased. For estimation of general non-linear parameters in small areas, we propose a model-based pseudo empirical best (PEB) method that incorporates the sampling weights and reduces considerably the bias of the unweighted empirical best (EB) estimators under informative selection mechanisms. We analyze the properties of this new method in simulation experiments carried out under complex sampling designs, including informative selection. Our results confirm that the proposed weighted PEB estimators perform significantly better than the unweighted EB estimators in terms of bias under informative sampling, and compare favorably under non-informative sampling. In an application to poverty mapping in Spain, we compare the proposed weighted PEB estimators with the unweighted EB analogues.

Suggested Citation

  • Rao, J.N.K. & Molina, Isabel & Guadarrama, María, 2016. "Small area estimation of general parameters under complex sampling designs," DES - Working Papers. Statistics and Econometrics. WS 22731, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:22731
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    References listed on IDEAS

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    1. Chris Elbers & Jean O. Lanjouw & Peter Lanjouw, 2003. "Micro--Level Estimation of Poverty and Inequality," Econometrica, Econometric Society, vol. 71(1), pages 355-364, January.
    2. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    3. repec:csb:stintr:v:17:y:2016:i:1:p:41-66 is not listed on IDEAS
    4. Jiang, Jiming & Lahiri, P., 2006. "Estimation of Finite Population Domain Means: A Model-Assisted Empirical Best Prediction Approach," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 301-311, March.
    5. 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.
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    Empirical best estimator;

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