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Non-area-specific adjustment factor for second-order efficient empirical Bayes confidence interval

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  • Hirose, Masayo Yoshimori

Abstract

An empirical Bayes confidence interval has high user demand in many applications. In particular, the second-order empirical Bayes confidence interval, the coverage error of which is of the third order for a large number of areas, m, is widely used in small area estimation when the sample size within each area is not large enough to make reliable direct estimates according to a design-based approach. Yoshimori and Lahiri (2014a) proposed a new type of confidence interval, called the second-order efficient empirical Bayes confidence interval, with a length less than that of the direct confidence estimated according to the design-based approach. However, this interval still has some disadvantages: (i) it is hard to use when at least one leverage value is high; (ii) many iterations tend to be required to obtain the estimators of one global model variance parameter as the number of areas, m, increases, due to the area-specific adjustment factor. To prevent such issues, this study proposes a more efficient confidence interval to allow for high leverage and reduce the number of iterations for large m. To achieve this purpose, we theoretically obtained a non-area-specific adjustment factor and the measure of uncertainty of the empirical Bayes estimator, which consist of empirical Bayes confidence interval, maintaining the existing desired properties. Moreover, we present three simulation results and real data analysis to show overall superiority of our confidence interval method over the other methods, including the one proposed in Yoshimori and Lahiri (2014a).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:116:y:2017:i:c:p:67-78
    DOI: 10.1016/j.csda.2017.07.002
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    References listed on IDEAS

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    1. Yoshitaka Sasase & Tatsuya Kubokawa, 2005. ""Asymptotic Correction of Empirical Bayes Confidence Intervals and its Application to Small Area Estimation" (in Japanese)," CIRJE J-Series CIRJE-J-127, CIRJE, Faculty of Economics, University of Tokyo.
    2. 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.
    3. 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.
    4. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
    5. 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.
    6. 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.
    7. 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.
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