IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v55y2014i3p653-670.html
   My bibliography  Save this article

Spatial robust small area estimation

Author

Listed:
  • Timo Schmid
  • Ralf Münnich

Abstract

The accuracy of recent applications in small area statistics in many cases highly depends on the assumed properties of the underlying models and the availability of micro information. In finite population sampling, small sample sizes may increase the sensitivity of the modeling with respect to single units. In these cases, area-specific sample sizes tend to be small such that normal assumptions, even of area means, seem to be violated. Hence, applying robust estimation methods is expected to yield more reliable results. In general, two robust small area methods are applied, the robust EBLUP and the M-quantile method. Additionally, the use of adequate auxiliary information may further increase the accuracy of the estimates. In prediction based approaches where information is needed on universe level, in general, only few variables are available which can be used for modeling. In addition to variables from the dataset, in many cases further information may be available, e.g. geographical information which could indicate spatial dependencies between neighboring areas. This spatial information can be included in the modeling using spatially correlated area effects. Within the paper the classical robust EBLUP is extended to cover spatial area effects via a simultaneous autoregressive model. The performance of the different estimators are compared in a model-based simulation study. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Timo Schmid & Ralf Münnich, 2014. "Spatial robust small area estimation," Statistical Papers, Springer, vol. 55(3), pages 653-670, August.
  • Handle: RePEc:spr:stpapr:v:55:y:2014:i:3:p:653-670
    DOI: 10.1007/s00362-013-0517-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-013-0517-y
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00362-013-0517-y?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. 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. Wojciech Niemiro & Jacek Wesołowski, 2010. "Synthetic and composite estimation under a superpopulation model," Statistical Papers, Springer, vol. 51(3), pages 497-509, September.
    3. Nikos Tzavidis & Nicola Salvati & Monica Pratesi & Ray Chambers, 2008. "M-quantile models with application to poverty mapping," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(3), pages 393-411, July.
    4. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, September.
    5. Martin Vogt & Ralf Munnich, 2009. "On the existence of a posterior distribution for spatial mixed models with binomial responses," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 201-209.
    6. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
    7. Manuel Landajo & Javier De Andrés & Pedro Lorca, 2008. "Measuring firm performance by using linear and non‐parametric quantile regressions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(2), pages 227-250, April.
    8. Ray Chambers & Nikos Tzavidis, 2006. "M-quantile models for small area estimation," Biometrika, Biometrika Trust, vol. 93(2), pages 255-268, June.
    9. 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.
    10. 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.
    11. 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.
    12. Despina Dasiou & Chronis Moyssiadis, 2001. "The 50% breakdown point in simultaneous M-estimation of location and scale," Statistical Papers, Springer, vol. 42(2), pages 243-252, April.
    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. Jan Pablo Burgard & Domingo Morales & Anna-Lena Wölwer, 2022. "Small area estimation of socioeconomic indicators for sampled and unsampled domains," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 287-314, June.
    2. Żądło Tomasz, 2020. "On Accuracy Estimation Using Parametric Bootstrap in small Area Prediction Problems," Journal of Official Statistics, Sciendo, vol. 36(2), pages 435-458, June.
    3. Saeideh Kamgar & Florian Meinfelder & Ralf Münnich & Hamidreza Navvabpour, 2020. "Estimation within the new integrated system of household surveys in Germany," Statistical Papers, Springer, vol. 61(5), pages 2091-2117, October.
    4. Jan Pablo Burgard & Joscha Krause & Dennis Kreber & Domingo Morales, 2021. "The generalized equivalence of regularization and min–max robustification in linear mixed models," Statistical Papers, Springer, vol. 62(6), pages 2857-2883, December.
    5. Huapeng Li & Yukun Liu & Riquan Zhang, 2019. "Small area estimation under transformed nested-error regression models," Statistical Papers, Springer, vol. 60(4), pages 1397-1418, August.
    6. 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.
    7. 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.
    8. 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.

    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. Ralf Münnich & Jan Burgard & Martin Vogt, 2013. "Small Area-Statistik: Methoden und Anwendungen," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 6(3), pages 149-191, March.
    2. 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.
    3. 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.
    4. 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.
    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. G. Bertarelli & R. Chambers & N. Salvati, 2021. "Outlier robust small domain estimation via bias correction and robust bootstrapping," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 331-357, March.
    7. 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.
    8. Merlo, Luca & Petrella, Lea & Salvati, Nicola & Tzavidis, Nikos, 2022. "Marginal M-quantile regression for multivariate dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    9. Stefano Marchetti & Caterina Giusti & Nicola Salvati & Monica Pratesi, 2017. "Small area estimation based on M-quantile models in presence of outliers in auxiliary variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 531-555, November.
    10. Paolo Frumento & Nicola Salvati, 2020. "Parametric modelling of M‐quantile regression coefficient functions with application to small area estimation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 229-250, January.
    11. 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.
    12. Sanjoy K. Sinha, 2019. "Robust small area estimation in generalized linear mixed models," METRON, Springer;Sapienza Università di Roma, vol. 77(3), pages 201-225, December.
    13. Muller, Christophe, 2018. "Heterogeneity and nonconstant effect in two-stage quantile regression," Econometrics and Statistics, Elsevier, vol. 8(C), pages 3-12.
    14. Otto-Sobotka, Fabian & Salvati, Nicola & Ranalli, Maria Giovanna & Kneib, Thomas, 2019. "Adaptive semiparametric M-quantile regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 116-129.
    15. Narula, Subhash C. & Wellington, John F. & Lewis, Stephen A., 2012. "Valuating residential real estate using parametric programming," European Journal of Operational Research, Elsevier, vol. 217(1), pages 120-128.
    16. Jean-Marc Fournier & Isabell Koske, 2012. "The determinants of earnings inequality: evidence from quantile regressions," OECD Journal: Economic Studies, OECD Publishing, vol. 2012(1), pages 7-36.
    17. 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.
    18. Duschl, Matthias & Schimke, Antje & Brenner, Thomas & Luxen, Dennis, 2011. "Firm growth and the spatial impact of geolocated external factors: Empirical evidence for German manufacturing firms," Working Paper Series in Economics 36, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    19. Boengiu, Tudor & Morar Triandafil, Cristina & Morar Triandafil, Adrian, 2011. "Debt Ceiling and External Debt Sustainability in Romania: A Quantile Autoregression Model," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 15-29, December.
    20. Ordu, Beyza Mina & Oran, Adil & Soytas, Ugur, 2018. "Is food financialized? Yes, but only when liquidity is abundant," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 82-96.

    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:spr:stpapr:v:55:y:2014:i:3:p:653-670. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.