IDEAS home Printed from https://ideas.repec.org/a/vrs/stintr/v18y2017i3p413-432n1.html
   My bibliography  Save this article

On Asymmetry of Prediction Errors in Small Area Estimation

Author

Listed:
  • Żądło Tomasz

    (University of Economics in Katowice, Faculty of Management, Katowice, Poland)

Abstract

The mean squared error reflects only the average prediction accuracy while the distribution of squared prediction error is positively skewed. Hence, assessing or comparing accuracy based on the MSE (which is the mean of squared errors) is insufficient and even inadequate because we should be interested not only in the average but in the whole distribution of prediction errors. This is the reason why we propose to use different than MSE measures of prediction accuracy in small area estimation. In the prediction accuracy comparisons we take into account our proposal for the empirical best predictor, which is a generalization of the predictor presented by Molina and Rao (2010). The generalization results from the assumption of a longitudinal model and possible changes of the population and subpopulations in time.

Suggested Citation

  • Żądło Tomasz, 2017. "On Asymmetry of Prediction Errors in Small Area Estimation," Statistics in Transition New Series, Polish Statistical Association, vol. 18(3), pages 413-432, September.
    • Handle: RePEc:vrs:stintr:v:18:y:2017:i:3:p:413-432:n:1
    DOI: 10.21307/stattrans-2016-078
    as

    Download full text from publisher

    File URL: https://doi.org/10.21307/stattrans-2016-078
    Download Restriction: no
    File URL: https://libkey.io/10.21307/stattrans-2016-078?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
    ---><---

    References listed on IDEAS

    as
    1. Gonzalez-Manteiga, W. & Lombardia, M.J. & Molina, I. & Morales, D. & Santamaria, L., 2007. "Estimation of the mean squared error of predictors of small area linear parameters under a logistic mixed model," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2720-2733, February.
    2. Jacqmin-Gadda, Helene & Sibillot, Solenne & Proust, Cecile & Molina, Jean-Michel & Thiebaut, Rodolphe, 2007. "Robustness of the linear mixed model to misspecified error distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5142-5154, June.
    Full references (including those not matched with items on IDEAS)

    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. Tomasz Żądło, 2017. "On Asymmetry Of Prediction Errors In Small Area Estimation," Statistics in Transition New Series, Polish Statistical Association, vol. 18(3), pages 413-432, September.
    2. Baumann, Elias & Kern, Jana & Lessmann, Stefan, 2019. "Usage Continuance in Software-as-a-Service," IRTG 1792 Discussion Papers 2019-005, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2020. "Small area estimation of proportions under area-level compositional mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 793-818, September.
    4. 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.
    5. Piyush Kant Rai & Sarla Pareek & Hemlata Joshi, 2017. "Met And Unmet Need For Contraception: Small Area Estimation For Rajasthan State Of India," Statistics in Transition New Series, Polish Statistical Association, vol. 18(2), pages 329-360, June.
    6. Viet-Thi Tran & Mariam Mama Djima & Eugene Messou & Jocelyne Moisan & Jean-Pierre Grégoire & Didier K Ekouevi, 2018. "Avoidable workload of care for patients living with HIV infection in Abidjan, Côte d’Ivoire: A cross-sectional study," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-15, August.
    7. Miguel Boubeta & María José Lombardía & Domingo Morales, 2016. "Empirical best prediction under area-level Poisson mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 548-569, September.
    8. Hukum Chandra, 2021. "District-Level Estimates of Poverty Incidence for the State of West Bengal in India: Application of Small Area Estimation Technique Combining NSSO Survey and Census Data," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(2), pages 375-391, June.
    9. Ralf Münnich & Jan Pablo Burgard & Siegfried Gabler & Matthias Ganninger & Jan-Philipp Kolb, 2016. "Small Area Estimation In The German Census 2011," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 25-40, March.
    10. Warrington Nicole M. & Tilling Kate & Howe Laura D. & Paternoster Lavinia & Pennell Craig E. & Wu Yan Yan & Briollais Laurent, 2014. "Robustness of the linear mixed effects model to error distribution assumptions and the consequences for genome-wide association studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(5), pages 1-21, October.
    11. Daniel McNeish & Jeffrey R. Harring & Denis Dumas, 2023. "A multilevel structured latent curve model for disaggregating student and school contributions to learning," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 545-575, June.
    12. Tomasz Ża̧dło, 2015. "On longitudinal moving average model for prediction of subpopulation total," Statistical Papers, Springer, vol. 56(3), pages 749-771, August.
    13. Elisabeth Veiz & Susann-Kristin Kieslich & Julia Staab & Dirk Czesnik & Christoph Herrmann-Lingen & Thomas Meyer, 2021. "Men Show Reduced Cardiac Baroreceptor Sensitivity during Modestly Painful Electrical Stimulation of the Forearm: Exploratory Results from a Sham-Controlled Crossover Vagus Nerve Stimulation Study," IJERPH, MDPI, vol. 18(21), pages 1-14, October.
    14. M. D. Ugarte & A. F. Militino & T. Goicoa, 2008. "Adjusting economic estimates in business surveys," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(11), pages 1253-1265.
    15. Angelo Moretti, 2023. "Estimation of small area proportions under a bivariate logistic mixed model," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(4), pages 3663-3684, August.
    16. 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.
    17. Molina, Isabel & Salvati, Nicola & Pratesi, Monica, 2007. "Bootstrap for estimating the mean squared error of the spatial EBLUP," DES - Working Papers. Statistics and Econometrics. WS ws073408, Universidad Carlos III de Madrid. Departamento de Estadística.
    18. repec:csb:stintr:v:17:y:2016:i:1:p:25-40 is not listed on IDEAS
    19. Katarzyna Reluga & María‐José Lombardía & Stefan Sperlich, 2023. "Simultaneous inference for linear mixed model parameters with an application to small area estimation," International Statistical Review, International Statistical Institute, vol. 91(2), pages 193-217, August.
    20. María Dolores Esteban & María José Lombardía & Esther López‐Vizcaíno & Domingo Morales & Agustín Pérez, 2022. "Empirical best prediction of small area bivariate parameters," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1699-1727, December.
    21. Boubeta, Miguel & Lombardía, María José & Morales, Domingo, 2017. "Poisson mixed models for studying the poverty in small areas," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 32-47.

    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:vrs:stintr:v:18:y:2017:i:3:p:413-432:n:1. 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: Peter Golla (email available below). General contact details of provider: https://www.sciendo.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.