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Coverage of generalized confidence intervals

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  • Roy, Anindya
  • Bose, Arup

Abstract

Generalized confidence intervals provide confidence intervals for complicated parametric functions in many common practical problems. They do not have exact frequentist coverage in general, but often provide coverage close to the nominal value and have the correct asymptotic coverage. However, in many applications generalized confidence intervals do not have satisfactory finite sample performance. We derive expansions of coverage probabilities of one-sided generalized confidence intervals and use the expansions to explain the nonuniform performance of the generalized intervals. We then show how to use these expansions to obtain improved coverage by suitable calibration. The benefits of the proposed modification are illustrated via several examples.

Suggested Citation

  • Roy, Anindya & Bose, Arup, 2009. "Coverage of generalized confidence intervals," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1384-1397, August.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:7:p:1384-1397
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    References listed on IDEAS

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    1. Gamage, Jinadasa & Mathew, Thomas & Weerahandi, Samaradasa, 2004. "Generalized p-values and generalized confidence regions for the multivariate Behrens-Fisher problem and MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 177-189, January.
    2. Hannig, Jan & Iyer, Hari & Patterson, Paul, 2006. "Fiducial Generalized Confidence Intervals," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 254-269, March.
    3. K. Kurian & Thomas Mathew & G. Sebastian, 2008. "Generalized confidence intervals for process capability indices in the one-way random model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(1), pages 83-92, January.
    4. Lin, Shu-Hui & Lee, Jack C., 2003. "Exact tests in simple growth curve models and one-way ANOVA with equicorrelation error structure," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 351-368, February.
    5. Hari K. Iyer & C.M. Jack Wang & Thomas Mathew, 2004. "Models and Confidence Intervals for True Values in Interlaboratory Trials," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1060-1071, December.
    6. Samaradasa Weerahandi & Vance W. Berger, 1999. "Exact Inference for Growth Curves with Intraclass Correlation Structure," Biometrics, The International Biometric Society, vol. 55(3), pages 921-924, September.
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