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Multivariate Global-Local Priors for Small Area Estimation

Author

Listed:
  • Tamal Ghosh

    (Citibank, Tampa, FL 33610, USA)

  • Malay Ghosh

    (Department of Statistics, University of Florida, Gainesville, FL 32611, USA)

  • Jerry J. Maples

    (United States Bureau of the Census, Washington, DC 20233, USA)

  • Xueying Tang

    (Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA)

Abstract

It is now widely recognized that small area estimation (SAE) needs to be model-based. Global-local (GL) shrinkage priors for random effects are important in sparse situations where many areas’ level effects do not have a significant impact on the response beyond what is offered by covariates. We propose in this paper a hierarchical multivariate model with GL priors. We prove the propriety of the posterior density when the regression coefficient matrix has an improper uniform prior. Some concentration inequalities are derived for the tail probabilities of the shrinkage estimators. The proposed method is illustrated via both data analysis and simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:3:p:40-688:d:871104
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    References listed on IDEAS

    as
    1. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    2. Xueying Tang & Malay Ghosh & Neung Soo Ha & Joseph Sedransk, 2018. "Modeling Random Effects Using Global–Local Shrinkage Priors in Small Area Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1476-1489, October.
    3. 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.
    4. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    5. Nicholas G. Polson & James G. Scott, 2012. "Local shrinkage rules, Lévy processes and regularized regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 287-311, March.
    6. 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)

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