基于多项分布数据的排名有限样本与大样本推断及其在政党排名中的应用
Finite- and Large-Sample Inference for Ranks using Multinomial Data with an Application to Ranking Political Parties
AI总结：
本文针对多项分布数据下的排名不确定性问题，构建了有限样本有效的类别排名置信集及大样本近似有效的bootstrap置信集，经实证与模拟验证，有限样本置信集表现更优。
摘要：
通过选择数据揭示的偏好对不同类别进行排序是十分常见的做法，一个典型的例子是利用政治态度调查或民意测验中估算的各候选人或政党的支持率对其进行排名。由于这类排名是基于支持率的估计值而非真实值计算得出的，政治候选人或政党的真实排名可能存在相当大的不确定性。\n本文研究通过构建每个类别排名的置信集来处理这种不确定性的问题，既考虑了为特定类别排名构建边际置信集的问题，也考虑了为所有类别排名构建联合置信集的问题。本研究分析的一个显著特点是，我们利用数据的多项分布结构，开发了在有限样本下有效的置信集。此外，我们还开发了仅在大样本下近似有效的基于bootstrap（自助法）的置信集。\n我们运用所提出的方法，基于2019年澳大利亚选举调查的数据对澳大利亚的政党进行了排名。研究发现，即使在调查受访者较少的澳大利亚领地，以及/或者只有小比例调查受访者选择的政党的情况下，我们的有限样本置信集在整个政党排名中都具有信息价值。相比之下，基于bootstrap的置信集有时信息性会大幅降低。这些发现促使我们在一项由经验数据驱动的模拟研究中对这些方法进行比较，结果表明，我们的有限样本置信集通常表现优于大样本下基于bootstrap的对应方法，在与我们的实证应用相似的场景中尤为明显。
英文摘要：
It is common to rank different categories by means of preferences that are revealed through data on choices. A prominent example is the ranking of political candidates or parties using the estimated share of support each one receives in surveys or polls about political attitudes. Since these rankings are computed using estimates of the share of support rather than the true share of support, there may be considerable uncertainty concerning the true ranking of the political candidates or parties. In this paper, we consider the problem of accounting for such uncertainty by constructing confidence sets for the rank of each category. We consider both the problem of constructing marginal confidence sets for the rank of a particular category as well as simultaneous confidence sets for the ranks of all categories. A distinguishing feature of our analysis is that we exploit the multinomial structure of the data to develop confidence sets that are valid in finite samples. We additionally develop confidence sets using the bootstrap that are valid only approximately in large samples. We use our methodology to rank political parties in Australia using data from the 2019 Australian Election Survey. We find that our finite-sample confidence sets are informative across the entire ranking of political parties, even in Australian territories with few survey respondents and/or with parties that are chosen by only a small share of the survey respondents. In contrast, the bootstrap-based confidence sets may sometimes be considerably less informative. These findings motivate us to compare these methods in an empirically-driven simulation study, in which we conclude that our finite-sample confidence sets often perform better than their large-sample, bootstrap-based counterparts, especially in settings that resemble our empirical application.
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