Minimax confidence intervals for the binomial parameter. (English) Zbl 1031.62006
Summary: A game-theoretic approach to setting and solution of statistical problems is considered by the example of the confidence interval (CI) estimation problem for the parameter \(\theta\) of the binomial distribution \(B(n,\theta)\). The confidence probability (CP) and the minimax decision function (MDF) are constructed for any set of CIs. This differs from the classical approach where the CI is constructed for a given CP. CPs for fixed width CIs are given in tabulated form. One half of these CIs is shorter than classical CIs for the same CPs. The MDF under consideration enables the observation number to be reduced by about 1.5 times from the classical approach for the same reliability and accuracy.
MSC:
| 62C20 | Minimax procedures in statistical decision theory |
| 62F25 | Parametric tolerance and confidence regions |
| 91A40 | Other game-theoretic models |
Keywords:
Statistical game; Minimax decision function; Randomized decision function; Binomial parameter; Fixed width confidence intervalsReferences:
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