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Small area estimation of general parameters under complex sampling designs

Author

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

Abstract

When the probabilities of selecting individuals (units) for the sample depend on the outcome values, the selection mechanism is said to be informative. Under informative selection, individuals with certain outcome values appear more often in the sample and, as a consequence, usual inference based on the actual sample without appropriate weighting might be strongly biased. An extension of the empirical best (EB) method for estimation of general non-linear parameters in small areas that handles informative selection by incorporating the sampling weights is proposed. Properties of this new method under complex sampling designs, including informative selection, are analyzed. Results confirm that the proposed weighted estimators significantly reduce the bias of unweighted EB estimators under informative sampling, and compare favorably under non-informative sampling. The proposed method is illustrated through an application to poverty mapping in a State from Mexico.

Suggested Citation

  • Guadarrama, María & Molina, Isabel & Rao, J.N.K., 2018. "Small area estimation of general parameters under complex sampling designs," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 20-40.
    • Handle: RePEc:eee:csdana:v:121:y:2018:i:c:p:20-40
    DOI: 10.1016/j.csda.2017.11.007
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    References listed on IDEAS

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    1. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    2. María Guadarrama & Isabel Molina & J. N. K. Rao, 2016. "A Comparison Of Small Area Estimation Methods For Poverty Mapping," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 41-66, March.
    3. repec:csb:stintr:v:17:y:2016:i:1:p:41-66 is not listed on IDEAS
    4. 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.
    5. 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.
    6. 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.
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    Citations

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    Cited by:

    1. Paul Walter & Marcus Groß & Timo Schmid & Nikos Tzavidis, 2021. "Domain prediction with grouped income data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1501-1523, October.
    2. Adam Chwila & Tomasz Żądło, 2020. "On the choice of the number of Monte Carlo iterations and bootstrap replicates in Empirical Best Prediction," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 35-60, June.
    3. Agne Bikauskaite & Isabel Molina & Domingo Morales, 2022. "Multivariate mixture model for small area estimation of poverty indicators," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 724-755, December.
    4. Corral Rodas,Paul Andres & Molina,Isabel & Nguyen,Minh Cong, 2020. "Pull Your Small Area Estimates up by the Bootstraps," Policy Research Working Paper Series 9256, The World Bank.
    5. Isabel Molina & Paul Corral & Minh Nguyen, 2022. "Estimation of poverty and inequality in small areas: review and discussion," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1143-1166, December.
    6. Molina Isabel, 2020. "Discussion of “Small area estimation: its evolution in five decades”, by Malay Ghosh," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 40-44, August.
    7. Kawakubo, Yuki & Kobayashi, Genya, 2023. "Small area estimation of general finite-population parameters based on grouped data," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    8. Chwila Adam & Żądło Tomasz, 2020. "On the choice of the number of Monte Carlo iterations and bootstrap replicates in Empirical Best Prediction," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 35-60, June.
    9. Nora Würz & Timo Schmid & Nikos Tzavidis, 2022. "Estimating regional income indicators under transformations and access to limited population auxiliary information," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1679-1706, October.
    10. Isabel Molina, 2020. "Discussion of "Small area estimation: its evolution in five decades", by Malay Ghosh," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 40-44, August.

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