标题： 不完全排名数据的统计推断：等级依赖性粗粒度化的情况 显示英文标题

标题： Statistical Inference for Incomplete Ranking Data: The Case of Rank-Dependent Coarsening

摘要： 我们研究了统计推断中排名数据的问题，特别是排名聚合问题，假设样本是不完整的，即不包含所有的选择替代项。 与大多数现有方法不同，我们明确地建模了从完整排名转换为不完整排名的过程，我们将其称为粗化过程。 为此，我们提出了排名依赖粗化这一概念，该概念假设不完整排名是由将完整排名投影到随机子集上的排名产生的。 对于我们的模型的具体实例，其中完整排名是从Plackett-Luce分布中抽取的，并且观察值的形式为成对偏好，我们研究了各种排名聚合方法的表现。 除了有限样本设置下的预测准确性外，我们还通过理论研究了一致性问题，即当样本大小趋于无穷大时，尽管由于（未知的）粗化导致观察值存在潜在偏差，但能够恢复目标排名的能力。 显示英文摘要

摘要： We consider the problem of statistical inference for ranking data, specifically rank aggregation, under the assumption that samples are incomplete in the sense of not comprising all choice alternatives. In contrast to most existing methods, we explicitly model the process of turning a full ranking into an incomplete one, which we call the coarsening process. To this end, we propose the concept of rank-dependent coarsening, which assumes that incomplete rankings are produced by projecting a full ranking to a random subset of ranks. For a concrete instantiation of our model, in which full rankings are drawn from a Plackett-Luce distribution and observations take the form of pairwise preferences, we study the performance of various rank aggregation methods. In addition to predictive accuracy in the finite sample setting, we address the theoretical question of consistency, by which we mean the ability to recover a target ranking when the sample size goes to infinity, despite a potential bias in the observations caused by the (unknown) coarsening.