Split sample methods for constructing confidence intervals for binomial and Poisson parameters
Split sample methods for constructing confidence intervals for binomial and Poisson parameters
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用于构造二项式和泊松参数置信区间的分割样本方法
DOI：
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发表时间：
2014
期刊：
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通讯作者：
P. Hall
中科院分区：
文献类型：
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作者：
G. Decrouez;P. Hall
提出了一种新的方法来提高格型分布均值的置信度区间的覆盖精度。这项技术可以非常普遍地应用于改进现有的方法，尽管我们在估计二项式比例或泊松平均值的背景下对其进行了最详细的考虑，在这些情况下它特别有效。该方法受一个简单的理论结果的启发，该结果表明，通过将大小为n的原始样本分成两部分，大小为n1和n2=n−n1，并基于这两个子样本的平均值的置信度过程，覆盖误差作为n的函数的高度振荡行为在很大程度上被消除了。或许令人惊讶的是，这种方法不会增加置信度区间的宽度；通常情况下，宽度会略微减小。与预期相反，当我们的新方法被用于基于已经执行得非常好的现有技术来修改置信度区间时，它表现得很好-它通常显著地提高了它们的覆盖精度。每次将分裂样本方法应用于现有的置信度区间过程都会产生一种新技术。
We introduce a new method for improving the coverage accuracy of confidence intervals for means of lattice distributions. The technique can be applied very generally to enhance existing approaches, although we consider it in greatest detail in the context of estimating a binomial proportion or a Poisson mean, where it is particularly effective. The method is motivated by a simple theoretical result, which shows that, by splitting the original sample of size n into two parts, of sizes n1 and n2=n−n1 , and basing the confidence procedure on the average of the means of these two subsamples, the highly oscillatory behaviour of coverage error, as a function of n, is largely removed. Perhaps surprisingly, this approach does not increase confidence interval width; usually the width is slightly reduced. Contrary to what might be expected, our new method performs well when it is used to modify confidence intervals based on existing techniques that already perform very well—it typically improves significantly their coverage accuracy. Each application of the split sample method to an existing confidence interval procedure results in a new technique.