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On optimal confidence sets for parameters in discrete distributions

Author

Listed:
  • Habiger, Joshua D.
  • McCann, Melinda H.
  • Tebbs, Joshua M.

Abstract

In discrete distributions, the coverage probability and the expected length of an interval estimator often depend on the unknown parameter of interest. Some authors have suggested that “good” interval estimators should have mean coverage probability near the nominal level and small mean expected length, where the mean is taken over all possible values of the parameter. This paper uses these criteria to precisely define an optimal interval estimator and finds it in the single-parameter discrete distribution setting.

Suggested Citation

  • Habiger, Joshua D. & McCann, Melinda H. & Tebbs, Joshua M., 2013. "On optimal confidence sets for parameters in discrete distributions," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 297-303.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:297-303
    DOI: 10.1016/j.spl.2012.09.018
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    References listed on IDEAS

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    1. Agresti, Alan & Gottard, Anna, 2007. "Nonconservative exact small-sample inference for discrete data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6447-6458, August.
    2. Schafer, Chad M. & Stark, Philip B., 2009. "Constructing Confidence Regions of Optimal Expected Size," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1080-1089.
    3. Shalabh, 2006. "Exact Analysis of Discrete Data by K. F. Hirji," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(4), pages 1009-1009, October.
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