Agresti A, Min Y
Department of Statistics, University of Florida, Gainesville 32611-8545, USA.
Biometrics. 2001 Sep;57(3):963-71. doi: 10.1111/j.0006-341x.2001.00963.x.
The traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level. In constructing such intervals for parameters in discrete distributions, less conservative behavior results from inverting a single two-sided test than inverting two separate one-sided tests of half the nominal level each. We illustrate for a variety of discrete problems, including interval estimation of a binomial parameter, the difference and the ratio of two binomial parameters for independent samples, and the odds ratio.
置信区间的传统定义要求在参数的任何值处的覆盖概率至少为名义置信水平。在为离散分布中的参数构建此类区间时，与对两个单独的、名义水平各为一半的单侧检验进行反转相比，对单个双侧检验进行反转会导致不太保守的行为。我们针对各种离散问题进行说明，包括二项式参数的区间估计、独立样本的两个二项式参数的差值和比值以及优势比。
