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The efficiency of Buehler confidence limits

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  • Kabaila, Paul
  • Lloyd, Chris J.

Abstract

The Buehler 1-[alpha] upper confidence limit is as small as possible, subject to the constraints that (a) its coverage probability never falls below 1-[alpha] and (b) it is a non-decreasing function of a designated statistic T. We provide two new results concerning the influence of T on the efficiency of this confidence limit. Firstly, we extend the result of Kabaila (Statist. Probab. Lett. 52 (2001) 145) to prove that, for a wide class of Ts, the T which maximizes the large-sample efficiency of this confidence limit is itself an approximate 1-[alpha] upper confidence limit. Secondly, there may be ties among the possible values of T. We provide the result that breaking these ties by a sufficiently small modification cannot decrease the finite-sample efficiency of the Buehler confidence limit.

Suggested Citation

  • Kabaila, Paul & Lloyd, Chris J., 2003. "The efficiency of Buehler confidence limits," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 21-28, October.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:1:p:21-28
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    References listed on IDEAS

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    1. Kabaila, Paul, 2001. "Better Buehler confidence limits," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 145-154, April.
    2. Chris J. Lloyd & Paul Kabaila, 2003. "On the Optimality and Limitations of Buehler Bounds," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(2), pages 167-174, June.
    3. Harris, Bernard & Soms, Andrew P., 1991. "Theory and counterexamples for confidence limits on system reliability," Statistics & Probability Letters, Elsevier, vol. 11(5), pages 411-417, May.
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    Cited by:

    1. Kabaila, Paul, 2008. "Statistical properties of exact confidence intervals from discrete data using studentized test statistics," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 720-727, April.

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