Count data arising in various fields of applications are often under‐reported. Ignoring undercount naturally leads to biased estimators and inaccurate confidence intervals. In the presence of undercount, in this paper, we develop likelihood‐based methodologies for estimation of mean using validation data. The asymptotic distributions of the competing estimators of the mean are derived. The impact of ignoring undercount on the coverage and length of the confidence intervals is investigated using extensive numerical studies. Finally an analysis of heat mortality data is presented.

中文翻译：

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计数不足的泊松均值估计：双重抽样方法

在各个应用领域中产生的计数数据经常被低估。忽略计数不足自然会导致估计量有偏差和置信区间不准确。在存在计数不足的情况下，本文中，我们开发了基于似然性的方法来使用验证数据估算均值。推导了均值的竞争估计量的渐近分布。使用大量的数值研究来研究忽略计数不足对置信区间的覆盖范围和长度的影响。最后，对热死亡率数据进行了分析。