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On small area estimation under a sub-area level model

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  • Torabi, Mahmoud
  • Rao, J.N.K.

Abstract

We propose an extension of the well-known Fay and Herriot (1979) area level model to sub-area level. Not only this model may be used to estimate small area means by borrowing strength from related areas, but also by borrowing strength from sub-areas to obtain more efficient sub-area estimators. Model-based empirical best linear unbiased prediction (EBLUP) estimators are obtained from the BLUP estimators by replacing the model parameters by suitable estimators, using an iterative method based on weighted residual sum of squares. Second order approximations to the mean squared error (MSE) of the EBLUP estimators are obtained and then used to drive MSE estimators unbiased to second order. Results of simulation studies on the performance of the proposed estimators are also provided.

Suggested Citation

  • Torabi, Mahmoud & Rao, J.N.K., 2014. "On small area estimation under a sub-area level model," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 36-55.
    • Handle: RePEc:eee:jmvana:v:127:y:2014:i:c:p:36-55
    DOI: 10.1016/j.jmva.2014.02.001
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    References listed on IDEAS

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    1. Gauri Sankar Datta & J. N. K. Rao & David Daniel Smith, 2005. "On measuring the variability of small area estimators under a basic area level model," Biometrika, Biometrika Trust, vol. 92(1), pages 183-196, March.
    2. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    3. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
    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.
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    Cited by:

    1. K. Shuvo Bakar & Nicholas Biddle & Philip Kokic & Huidong Jin, 2020. "A Bayesian spatial categorical model for prediction to overlapping geographical areas in sample surveys," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 535-563, February.
    2. Newhouse David, 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 45-50, August.
    3. Erciulescu Andreea L. & Cruze Nathan B. & Nandram Balgobin, 2020. "Statistical Challenges in Combining Survey and Auxiliary Data to Produce Official Statistics," Journal of Official Statistics, Sciendo, vol. 36(1), pages 63-88, March.
    4. Corral Rodas,Paul Andres & Kastelic,Kristen Himelein & Mcgee,Kevin Robert & Molina,Isabel, 2021. "A Map of the Poor or a Poor Map ?," Policy Research Working Paper Series 9620, The World Bank.
    5. Lu Chen & Balgobin Nandram, 2023. "Bayesian Logistic Regression Model for Sub-Areas," Stats, MDPI, vol. 6(1), pages 1-23, January.
    6. Newhouse,David Locke & Merfeld,Joshua David & Ramakrishnan,Anusha Pudugramam & Swartz,Tom & Lahiri,Partha, 2022. "Small Area Estimation of Monetary Poverty in Mexico Using Satellite Imagery and Machine Learning," Policy Research Working Paper Series 10175, The World Bank.
    7. Song Cai & J.N.K. Rao, 2022. "Selection of Auxiliary Variables for Three-Fold Linking Models in Small Area Estimation: A Simple and Effective Method," Stats, MDPI, vol. 5(1), pages 1-11, February.
    8. Lu Chen & Luca Sartore & Habtamu Benecha & Valbona Bejleri & Balgobin Nandram, 2022. "Smoothing County-Level Sampling Variances to Improve Small Area Models’ Outputs," Stats, MDPI, vol. 5(3), pages 1-18, September.
    9. Lu Chen & Nathan B. Cruze & Linda J. Young, 2022. "Model-Based Estimates for Farm Labor Quantities," Stats, MDPI, vol. 5(3), pages 1-17, August.
    10. Paul Corral & Kristen Himelein & Kevin McGee & Isabel Molina, 2021. "A Map of the Poor or a Poor Map?," Mathematics, MDPI, vol. 9(21), pages 1-40, November.
    11. Cai Song & Rao J. N. K. & Dumitrescu Laura & Chatrchi Golshid, 2020. "Effective transformation-based variable selection under two-fold subarea models in small area estimation," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 68-83, August.
    12. Jae Kwang Kim & Zhonglei Wang & Zhengyuan Zhu & Nathan B. Cruze, 2018. "Combining Survey and Non-survey Data for Improved Sub-area Prediction Using a Multi-level Model," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(2), pages 175-189, June.
    13. Linda J. Young & Lu Chen, 2022. "Using Small Area Estimation to Produce Official Statistics," Stats, MDPI, vol. 5(3), pages 1-17, September.
    14. Song Cai & J. N. K. Rao & Laura Dumitrescu & Golshid Chatrchi, 2020. "Effective transformation-based variable selection under two-fold subarea models in small area estimation," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 68-83, August.
    15. Batana,Yele Maweki & Masaki,Takaaki & Nakamura,Shohei & Viboudoulou Vilpoux,Mervy Ever, 2021. "Estimating Poverty in Kinshasa by Dealing with Sampling and Comparability Issues," Policy Research Working Paper Series 9858, The World Bank.
    16. Masaki,Takaaki & Newhouse,David Locke & Silwal,Ani Rudra & Bedada,Adane & Engstrom,Ryan, 2020. "Small Area Estimation of Non-Monetary Poverty with Geospatial Data," Policy Research Working Paper Series 9383, The World Bank.

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