IDEAS home Printed from https://ideas.repec.org/a/vrs/stintr/v17y2016i1p67-90n5.html
   My bibliography  Save this article

A Two-Component Normal Mixture Alternative to the Fay-Herriot Model

Author

Listed:
  • Chakraborty Adrijo

    (NORC at the University of Chicago, Bethesda, MD 20814 ; United States)

  • Datta Gauri Sankar

    (Department of Statistics, University of Georgia, Athens, GA 30602, United States)

  • Mandal Abhyuday

    (Department of Statistics, University of Georgia, Athens, GA 30602, United States)

Abstract

This article considers a robust hierarchical Bayesian approach to deal with random effects of small area means when some of these effects assume extreme values, resulting in outliers. In the presence of outliers, the standard Fay-Herriot model, used for modeling area-level data, under normality assumptions of random effects may overestimate the random effects variance, thus providing less than ideal shrinkage towards the synthetic regression predictions and inhibiting the borrowing of information. Even a small number of substantive outliers of random effects results in a large estimate of the random effects variance in the Fay-Herriot model, thereby achieving little shrinkage to the synthetic part of the model or little reduction in the posterior variance associated with the regular Bayes estimator for any of the small areas. While the scale mixture of normal distributions with a known mixing distribution for the random effects has been found to be effective in the presence of outliers, the solution depends on the mixing distribution. As a possible alternative solution to the problem, a two-component normal mixture model has been proposed, based on non-informative priors on the model variance parameters, regression coefficients and the mixing probability. Data analysis and simulation studies based on real, simulated and synthetic data show an advantage of the proposed method over the standard Bayesian Fay-Herriot solution derived under normality of random effects.

Suggested Citation

  • Chakraborty Adrijo & Datta Gauri Sankar & Mandal Abhyuday, 2016. "A Two-Component Normal Mixture Alternative to the Fay-Herriot Model," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 67-90, March.
  • Handle: RePEc:vrs:stintr:v:17:y:2016:i:1:p:67-90:n:5
    DOI: 10.21307/stattrans-2016-006
    as

    Download full text from publisher

    File URL: https://doi.org/10.21307/stattrans-2016-006
    Download Restriction: no

    File URL: https://libkey.io/10.21307/stattrans-2016-006?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
    ---><---

    References listed on IDEAS

    as
    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. Malay Ghosh & Tapabrata Maiti & Ananya Roy, 2008. "Influence functions and robust Bayes and empirical Bayes small area estimation," Biometrika, Biometrika Trust, vol. 95(3), pages 573-585.
    3. Ray Chambers & Hukum Chandra & Nicola Salvati & Nikos Tzavidis, 2014. "Outlier robust small area estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 47-69, January.
    4. Datta, Gauri S. & Hall, Peter & Mandal, Abhyuday, 2011. "Model Selection by Testing for the Presence of Small-Area Effects, and Application to Area-Level Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 362-374.
    5. 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.
    6. Datta, G. S. & Lahiri, P., 1995. "Robust Hierarchical Bayes Estimation of Small Area Characteristics in the Presence of Covariates and Outliers," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 310-328, August.
    7. Gauri Sankar Datta & Abhyuday Mandal, 2015. "Small Area Estimation With Uncertain Random Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1735-1744, 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. repec:csb:stintr:v:17:y:2016:i:1:p:67-90 is not listed on IDEAS
    2. Adrijo Chakraborty & Gauri Sankar Datta & Abhyuday Mandal, 2016. "A Two-Component Normal Mixture Alternative To The Fay-Herriot Model," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 67-90, March.
    3. 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.
    4. Malay Ghosh, 2020. "Small area estimation: its evolution in five decades," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 1-22, August.
    5. Sugasawa, Shonosuke & Kubokawa, Tatsuya, 2017. "Transforming response values in small area prediction," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 47-60.
    6. Shonosuke Sugasawa & Tatsuya Kubokawa & Kota Ogasawara, 2017. "Empirical Uncertain Bayes Methods in Area-level Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 684-706, September.
    7. Ghosh Malay, 2020. "Small area estimation: its evolution in five decades," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 1-22, August.
    8. 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.
    9. Sun, Hanmei & Jiang, Jiming & Nguyen, Thuan & Luan, Yihui, 2018. "Best look-alike prediction: Another look at the Bayesian classifier and beyond," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 37-42.
    10. Nikos Tzavidis & Li‐Chun Zhang & Angela Luna & Timo Schmid & Natalia Rojas‐Perilla, 2018. "From start to finish: a framework for the production of small area official statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 927-979, October.
    11. Tamal Ghosh & Malay Ghosh & Jerry J. Maples & Xueying Tang, 2022. "Multivariate Global-Local Priors for Small Area Estimation," Stats, MDPI, vol. 5(3), pages 1-16, July.
    12. 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.
    13. Lixia Diao & David D. Smith & Gauri Sankar Datta & Tapabrata Maiti & Jean D. Opsomer, 2014. "Accurate Confidence Interval Estimation of Small Area Parameters Under the Fay–Herriot Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 497-515, June.
    14. Sugasawa, Shonosuke & Kubokawa, Tatsuya, 2017. "Bayesian estimators in uncertain nested error regression models," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 52-63.
    15. Yoshimori, Masayo & Lahiri, Partha, 2014. "A new adjusted maximum likelihood method for the Fay–Herriot small area model," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 281-294.
    16. 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.
    17. Stefano Marchetti & Caterina Giusti & Monica Pratesi, 2016. "The use of Twitter data to improve small area estimates of households’ share of food consumption expenditure in Italy [Die Nutzung von Twitter Daten um die Small Area Schätzungen vom Ausgabenanteil," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 10(2), pages 79-93, October.
    18. Elżbieta Gołata, 2015. "Sae Education Challenges To Academics And Nsi," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 611-630, December.
    19. Sugasawa, Shonosuke & Kubokawa, Tatsuya, 2015. "Parametric transformed Fay–Herriot model for small area estimation," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 295-311.
    20. Fernando A. S. Moura & André Felipe Neves & Denise Britz do N. Silva, 2017. "Small area models for skewed Brazilian business survey data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1039-1055, October.
    21. 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.

    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:17:y:2016:i:1:p:67-90:n:5. 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://stat.gov.pl/en/ .

    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.