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Accurate Confidence Interval Estimation of Small Area Parameters Under the Fay–Herriot Model

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Listed:
  • Lixia Diao
  • David D. Smith
  • Gauri Sankar Datta
  • Tapabrata Maiti
  • Jean D. Opsomer

Abstract

type="main" xml:id="sjos12045-abs-0001"> Small area estimation has long been a popular and important research topic due to its growing demand in public and private sectors. We consider here the basic area level model, popularly known as the Fay–Herriot model. Although much of current research is predominantly focused on second order unbiased estimation of mean squared prediction errors, we concentrate on developing confidence intervals (CIs) for the small area means that are second order correct. The corrected CI can be readily implemented, because it only requires quantities that are already estimated as part of the mean squared error estimation. We extend the approach to a CI for the difference of two small area means. The findings are illustrated with a simulation study.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:2:p:497-515
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    References listed on IDEAS

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    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. Gauri Sankar Datta & Malay Ghosh & David Daniel Smith & Parthasarathi Lahiri, 2002. "On an Asymptotic Theory of Conditional and Unconditional Coverage Probabilities of Empirical Bayes Confidence Intervals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 139-152, March.
    3. 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.
    4. Gauri Sankar Datta & J. N. K. Rao & David Daniel Smith, 2012. "On measuring the variability of small area estimators under a basic area level model," Biometrika, Biometrika Trust, vol. 99(2), pages 509-509.
    5. Nankervis, John C., 2005. "Computational algorithms for double bootstrap confidence intervals," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 461-475, April.
    6. Peter Hall & Stephen M.‐S. Lee & G. Alastair Young, 2000. "Importance of interpolation when constructing double‐bootstrap confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 479-491.
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    Cited by:

    1. Hirose, Masayo Yoshimori, 2017. "Non-area-specific adjustment factor for second-order efficient empirical Bayes confidence interval," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 67-78.
    2. Sugasawa, Shonosuke & Kubokawa, Tatsuya, 2017. "Transforming response values in small area prediction," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 47-60.
    3. 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.

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