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

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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
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    File URL: http://www.uni-trier.de/fileadmin/fb4/prof/VWL/EWF/Research_Papers/2019-04.pdf
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    References listed on IDEAS

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    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

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    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. 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. 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).

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