IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i10p2875-2888.html
   My bibliography  Save this article

Small area estimation under spatial nonstationarity

Author

Listed:
  • Chandra, Hukum
  • Salvati, Nicola
  • Chambers, Ray
  • Tzavidis, Nikos

Abstract

A geographical weighted empirical best linear unbiased predictor (GWEBLUP) for a small area average is proposed, and an estimator of its conditional mean squared error is developed. The popular empirical best linear unbiased predictor under the linear mixed model is obtained as a special case of the GWEBLUP. Empirical results using both model-based and design-based simulations, with the latter based on two real data sets, show that the GWEBLUP predictor can lead to efficiency gains when spatial nonstationarity is present in the data. A practical gain from using the GWEBLUP is in small area estimation for out of sample areas. In this case the efficient use of geographical information can potentially improve upon conventional synthetic estimation.

Suggested Citation

  • Chandra, Hukum & Salvati, Nicola & Chambers, Ray & Tzavidis, Nikos, 2012. "Small area estimation under spatial nonstationarity," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2875-2888.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:10:p:2875-2888
    DOI: 10.1016/j.csda.2012.02.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312000734
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.02.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Noel Cressie & Gardar Johannesson, 2008. "Fixed rank kriging for very large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 209-226, February.
    2. Ray Chambers & Nikos Tzavidis, 2006. "M-quantile models for small area estimation," Biometrika, Biometrika Trust, vol. 93(2), pages 255-268, June.
    3. Monica Pratesi & Nicola Salvati, 2008. "Small area estimation: the EBLUP estimator based on spatially correlated random area effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 113-141, February.
    4. Ugarte, M.D. & Goicoa, T. & Militino, A.F. & Durbán, M., 2009. "Spline smoothing in small area trend estimation and forecasting," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3616-3629, August.
    5. Salvati, Nicola & Chandra, Hukum & Giovanna Ranalli, M. & Chambers, Ray, 2010. "Small area estimation using a nonparametric model-based direct estimator," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2159-2171, September.
    6. J. D. Opsomer & G. Claeskens & M. G. Ranalli & G. Kauermann & F. J. Breidt, 2008. "Non‐parametric small area estimation using penalized spline regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 265-286, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Isabel Molina & Ewa Strzalkowska‐Kominiak, 2020. "Estimation of proportions in small areas: application to the labour force using the Swiss Census Structural Survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 281-310, January.
    2. 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).
    3. Timo Schmid & Nikos Tzavidis & Ralf Münnich & Ray Chambers, 2016. "Outlier Robust Small-Area Estimation Under Spatial Correlation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 806-826, September.
    4. Baldermann, Claudia & Salvati, Nicola & Schmid, Timo, 2016. "Robust small area estimation under spatial non-stationarity," Discussion Papers 2016/5, Free University Berlin, School of Business & Economics.
    5. Schmid, Timo & Tzavidis, Nikos & Münnich, Ralf & Chambers, Ray, 2015. "Outlier robust small area estimation under spatial correlation," Discussion Papers 2015/8, Free University Berlin, School of Business & Economics.
    6. Tomasz .Zk{a}d{l}o & Adam Chwila, 2024. "A step towards the integration of machine learning and small area estimation," Papers 2402.07521, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. N. Salvati & N. Tzavidis & M. Pratesi & R. Chambers, 2012. "Small area estimation via M-quantile geographically weighted regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 1-28, March.
    2. María José Lombardía & Esther López‐Vizcaíno & Cristina Rueda, 2017. "Mixed generalized Akaike information criterion for small area models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1229-1252, October.
    3. Tapabrata Maiti & Samiran Sinha & Ping-Shou Zhong, 2016. "Functional Mixed Effects Model for Small Area Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 886-903, September.
    4. Baldermann, Claudia & Salvati, Nicola & Schmid, Timo, 2016. "Robust small area estimation under spatial non-stationarity," Discussion Papers 2016/5, Free University Berlin, School of Business & Economics.
    5. Shonosuke Sugasawa & Tatsuya Kubokawa & J. N. K. Rao, 2018. "Small area estimation via unmatched sampling and linking models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 407-427, June.
    6. J. N. K. Rao, 2015. "Inferential issues in model-based small area estimation: some new developments," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 491-510, December.
    7. Valéry Dongmo Jiongo & Pierre Nguimkeu, 2018. "Bootstrapping Mean Squared Errors of Robust Small-Area Estimators: Application to the Method-of-Payments Data," Staff Working Papers 18-28, Bank of Canada.
    8. 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.
    9. Tomasz Ża̧dło, 2015. "On longitudinal moving average model for prediction of subpopulation total," Statistical Papers, Springer, vol. 56(3), pages 749-771, August.
    10. Ranjbar, Setareh & Salvati, Nicola & Pacini, Barbara, 2023. "Estimating heterogeneous causal effects in observational studies using small area predictors," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    11. Salvati, Nicola & Chandra, Hukum & Giovanna Ranalli, M. & Chambers, Ray, 2010. "Small area estimation using a nonparametric model-based direct estimator," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2159-2171, September.
    12. María José Lombardía & Esther López-Vizcaíno & Cristina Rueda, 2021. "Selection model for domains across time: application to labour force survey by economic activities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 228-254, March.
    13. J. N. K. Rao, 2015. "Inferential Issues In Model-Based Small Area Estimation: Some New Developments," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 491-510, December.
    14. Szymkowiak Marcin & Młodak Andrzej & Wawrowski Łukasz, 2017. "Mapping Poverty at the Level of Subregions in Poland Using Indirect Estimation," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 609-635, December.
    15. Tzavidis, Nikos & Zhang, Li-Chun & Luna Hernandez, Angela & Schmid, Timo & Rojas-Perilla, Natalia, 2016. "From start to finish: A framework for the production of small area official statistics," Discussion Papers 2016/13, Free University Berlin, School of Business & Economics.
    16. Chandra, Hukum & Salvati, Nicola & Chambers, Ray, 2018. "Small area estimation under a spatially non-linear model," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 19-38.
    17. Caterina Giusti & Lucio Masserini & Monica Pratesi, 2017. "Local Comparisons of Small Area Estimates of Poverty: An Application Within the Tuscany Region in Italy," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 131(1), pages 235-254, March.
    18. Schmid, Timo & Tzavidis, Nikos & Münnich, Ralf & Chambers, Ray, 2015. "Outlier robust small area estimation under spatial correlation," Discussion Papers 2015/8, Free University Berlin, School of Business & Economics.
    19. Timo Schmid & Ralf Münnich, 2014. "Spatial robust small area estimation," Statistical Papers, Springer, vol. 55(3), pages 653-670, August.
    20. Marcin Szymkowiak & Andrzej Młodak & Łukasz Wawrowski, 2017. "Mapping Poverty At The Level Of Subregions In Poland Using Indirect Estimation," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 609-635, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:10:p:2875-2888. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.