IDEAS home Printed from https://ideas.repec.org/p/trr/wpaper/201904.html
   My bibliography  Save this paper

Regularized Area-level Modelling for Robust Small Area Estimation in the Presence of Unknown Covariate Measurement Errors

Author

Listed:
  • Jan Pablo Burgard
  • Joscha Krause
  • Dennis Kreber

Abstract

An approach to model-based small area estimation under covariate measurement errors is presented. Using a min-max approach, we proof that regularized regression coefficient estimation is equivalent to robust optimization under additive noise. Applying this equivalence, the Fay-Herriot model is extended by t'1-norm, squared t'2-norm and elastic net regularizations as robustification against design matrix perturbations. This allows for reliable area-statistic estimates without distributive information about the measurement errors. A best predictor and a Jackknife estimator of the mean squared error are presented. The methodology is evaluated in a simulation study under multiple measurement error scenarios to support the theoretical findings. A comparison to other robust small area approaches is conducted. An empirical ap- plication to poverty mapping in the US is provided. Estimated economic figures from the US Census Bureau and crime records from the Uniform Crime Reporting Program are used to model the number of citizens below the federal poverty threshold.

Suggested Citation

  • Jan Pablo Burgard & Joscha Krause & Dennis Kreber, 2019. "Regularized Area-level Modelling for Robust Small Area Estimation in the Presence of Unknown Covariate Measurement Errors," Research Papers in Economics 2019-04, University of Trier, Department of Economics.
    • Handle: RePEc:trr:wpaper:201904
    as

    Download full text from publisher

    File URL: http://www.uni-trier.de/fileadmin/fb4/prof/VWL/EWF/Research_Papers/2019-04.pdf
    File Function: First version, 2019
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bertsimas, Dimitris & Copenhaver, Martin S., 2018. "Characterization of the equivalence of robustification and regularization in linear and matrix regression," European Journal of Operational Research, Elsevier, vol. 270(3), pages 931-942.
    2. Lynn M. R. Ybarra & Sharon L. Lohr, 2008. "Small area estimation when auxiliary information is measured with error," Biometrika, Biometrika Trust, vol. 95(4), pages 919-931.
    3. 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.
    4. Li, Huilin & Lahiri, P., 2010. "An adjusted maximum likelihood method for solving small area estimation problems," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 882-892, April.
    5. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    6. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    7. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, 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. Burgard, Jan Pablo & Krause, Joscha & Schmaus, Simon, 2021. "Estimation of regional transition probabilities for spatial dynamic microsimulations from survey data lacking in regional detail," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).
    2. 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.
    3. Jan Pablo Burgard & Joscha Krause & Ralf Münnich, 2019. "Penalized Small Area Models for the Combination of Unit- and Area-level Data," Research Papers in Economics 2019-05, University of Trier, Department of Economics.
    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.

    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. Joscha Krause & Jan Pablo Burgard & Domingo Morales, 2022. "Robust prediction of domain compositions from uncertain data using isometric logratio transformations in a penalized multivariate Fay–Herriot model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 65-96, February.
    2. Jan Pablo Burgard & Joscha Krause & Ralf Münnich, 2019. "Penalized Small Area Models for the Combination of Unit- and Area-level Data," Research Papers in Economics 2019-05, University of Trier, Department of Economics.
    3. 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.
    4. Kreutzmann, Ann-Kristin & Marek, Philipp & Salvati, Nicola & Schmid, Timo, 2019. "Estimating regional wealth in Germany: How different are East and West really?," Discussion Papers 35/2019, Deutsche Bundesbank.
    5. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    6. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.
    7. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
    8. Chuliá, Helena & Garrón, Ignacio & Uribe, Jorge M., 2024. "Daily growth at risk: Financial or real drivers? The answer is not always the same," International Journal of Forecasting, Elsevier, vol. 40(2), pages 762-776.
    9. Christopher J Greenwood & George J Youssef & Primrose Letcher & Jacqui A Macdonald & Lauryn J Hagg & Ann Sanson & Jenn Mcintosh & Delyse M Hutchinson & John W Toumbourou & Matthew Fuller-Tyszkiewicz &, 2020. "A comparison of penalised regression methods for informing the selection of predictive markers," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-14, November.
    10. Immanuel Bayer & Philip Groth & Sebastian Schneckener, 2013. "Prediction Errors in Learning Drug Response from Gene Expression Data – Influence of Labeling, Sample Size, and Machine Learning Algorithm," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-13, July.
    11. Mostafa Rezaei & Ivor Cribben & Michele Samorani, 2021. "A clustering-based feature selection method for automatically generated relational attributes," Annals of Operations Research, Springer, vol. 303(1), pages 233-263, August.
    12. Gustavo A. Alonso-Silverio & Víctor Francisco-García & Iris P. Guzmán-Guzmán & Elías Ventura-Molina & Antonio Alarcón-Paredes, 2021. "Toward Non-Invasive Estimation of Blood Glucose Concentration: A Comparative Performance," Mathematics, MDPI, vol. 9(20), pages 1-13, October.
    13. Christopher Kath & Florian Ziel, 2018. "The value of forecasts: Quantifying the economic gains of accurate quarter-hourly electricity price forecasts," Papers 1811.08604, arXiv.org.
    14. 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.
    15. Karim Barigou & Stéphane Loisel & Yahia Salhi, 2020. "Parsimonious Predictive Mortality Modeling by Regularization and Cross-Validation with and without Covid-Type Effect," Risks, MDPI, vol. 9(1), pages 1-18, December.
    16. Gurgul Henryk & Machno Artur, 2017. "Trade Pattern on Warsaw Stock Exchange and Prediction of Number of Trades," Statistics in Transition New Series, Statistics Poland, vol. 18(1), pages 91-114, March.
    17. 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.
    18. Michael Funke & Kadri Männasoo & Helery Tasane, 2023. "Regional Economic Impacts of the Øresund Cross-Border Fixed Link: Cui Bono?," CESifo Working Paper Series 10557, CESifo.
    19. Camila Epprecht & Dominique Guegan & Álvaro Veiga & Joel Correa da Rosa, 2017. "Variable selection and forecasting via automated methods for linear models: LASSO/adaLASSO and Autometrics," Post-Print halshs-00917797, HAL.
    20. Zichen Zhang & Ye Eun Bae & Jonathan R. Bradley & Lang Wu & Chong Wu, 2022. "SUMMIT: An integrative approach for better transcriptomic data imputation improves causal gene identification," Nature Communications, Nature, vol. 13(1), pages 1-12, 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:trr:wpaper:201904. 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: Matthias Neuenkirch (email available below). General contact details of provider: https://edirc.repec.org/data/petride.html .

    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.