IDEAS home Printed from https://ideas.repec.org/a/vrs/offsta/v34y2018i2p523-542n12.html
   My bibliography  Save this article

Small Area Estimation with a Lognormal Mixed Model under Informative Sampling

Author

Listed:
  • Zimmermann Thomas

    (Statistisches Bundesamt, Mathematical-Statistical Methods & Research Data Centre, Gustav-Stresemann-Ring 11, D-65189Wiesbaden, Germany.)

  • Münnich Ralf Thomas

    (University of Trier, Faculty IV – Economics, Economic and Social Statistics Department, Universitätsring 15, D-54286Trier, Germany.)

Abstract

The demand for reliable business statistics at disaggregated levels, such as industry classes, increased considerably in recent years. Owing to small sample sizes for some of the domains, design-based methods may not provide estimates with adequate precision. Hence, modelbased small area estimation techniques that increase the effective sample size by borrowing strength are needed. Business data are frequently characterised by skewed distributions, with a few large enterprises that account for the majority of the total for the variable of interest, for example turnover. Moreover, the relationship between the variable of interest and the auxiliary variables is often non-linear on the original scale. In many cases, a lognormal mixed model provides a reasonable approximation of this relationship. In this article, we extend the empirical best prediction (EBP) approach to compensate for informative sampling, by incorporating design information among the covariates via an augmented modelling approach. This gives rise to the EBP under the augmented model. We propose to select the augmenting variable based on a joint assessment of a measure of predictive accuracy and a check of the normality assumptions. Finally, we compare our approach with alternatives in a model-based simulation study under different informative sampling mechanisms.

Suggested Citation

  • Zimmermann Thomas & Münnich Ralf Thomas, 2018. "Small Area Estimation with a Lognormal Mixed Model under Informative Sampling," Journal of Official Statistics, Sciendo, vol. 34(2), pages 523-542, June.
  • Handle: RePEc:vrs:offsta:v:34:y:2018:i:2:p:523-542:n:12
    DOI: 10.2478/jos-2018-0024
    as

    Download full text from publisher

    File URL: https://doi.org/10.2478/jos-2018-0024
    Download Restriction: no

    File URL: https://libkey.io/10.2478/jos-2018-0024?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. Berg, Emily & Chandra, Hukum, 2014. "Small area prediction for a unit-level lognormal model," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 159-175.
    2. Alfons, Andreas & Templ, Matthias & Filzmoser, Peter, 2010. "An Object-Oriented Framework for Statistical Simulation: The R Package simFrame," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 37(i03).
    3. 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.
    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. 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.
    2. 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.
    3. Rao J. N. K., 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.
    4. Dian Handayani & Henk Folmer & Anang Kurnia & Khairil Anwar Notodiputro, 2018. "The spatial empirical Bayes predictor of the small area mean for a lognormal variable of interest and spatially correlated random effects," Empirical Economics, Springer, vol. 55(1), pages 147-167, August.
    5. repec:csb:stintr:v:17:y:2016:i:1:p:133-154 is not listed on IDEAS
    6. Silvia De Nicol`o & Maria Rosaria Ferrante & Silvia Pacei, 2021. "Mind the Income Gap: Bias Correction of Inequality Estimators in Small-Sized Samples," Papers 2107.08950, arXiv.org, revised May 2023.
    7. Michael A. Hidiroglou & Victor M. Estevao, 2016. "A Comparison Of Small Area And Calibration Estimators Via Simulation," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 133-154, March.
    8. 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.
    9. Alfons, Andreas & Croux, Christophe & Gelper, Sarah, 2016. "Robust groupwise least angle regression," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 421-435.
    10. 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.
    11. J. N. K. Rao, 2021. "On Making Valid Inferences by Integrating Data from Surveys and Other Sources," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 242-272, May.
    12. Alfons, Andreas & Templ, Matthias, 2013. "Estimation of Social Exclusion Indicators from Complex Surveys: The R Package laeken," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i15).
    13. Hidiroglou M. A. & Estevao V. M., 2016. "A Comparison of Small Area and Calibration Estimators Via Simulation," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 133-154, March.
    14. Hofert, Marius & Mächler, Martin, 2016. "Parallel and Other Simulations in R Made Easy: An End-to-End Study," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i04).
    15. 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.
    16. Feng Wang & HaiYing Wang & Jun Yan, 2023. "Diagnostic Tests for the Necessity of Weight in Regression With Survey Data," International Statistical Review, International Statistical Institute, vol. 91(1), pages 55-71, April.
    17. Burgard Jan Pablo & Münnich Ralf & Zimmermann Thomas, 2014. "The Impact of Sampling Designs on Small Area Estimates for Business Data," Journal of Official Statistics, Sciendo, vol. 30(4), pages 749-771, December.
    18. Isabel Molina & Malay Ghosh, 2021. "Accounting for dependent informative sampling in model-based finite population inference," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 179-197, March.
    19. Kowarik, Alexander & Templ, Matthias, 2016. "Imputation with the R Package VIM," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 74(i07).
    20. 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.
    21. Berg Emily, 2022. "Construction of Databases for Small Area Estimation," Journal of Official Statistics, Sciendo, vol. 38(3), pages 673-708, September.

    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:offsta:v:34:y:2018:i:2:p:523-542:n:12. 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.