This paper proposes an econometric method to construct confidence sets for rankings by considering the situations in which data on a comparison between each pair of alternatives are available. The key idea is that if an alternative, say A, is ranked higher than some other alternative, say B, then it would be natural to assume that drawing an observation in which A is compared favorably with B is more likely than the opposite. This provides an insight that we can use to test for a particular ranking by translating it into a problem of testing moment inequalities and that we can obtain confidence sets for rankings by inverting these tests of moment inequalities. We apply the proposed method to statistical inference concerning the rankings of teams in the Nippon Professional Baseball league in Japan.

本文提出一种计量经济学的方法，通过考虑可获得每对替代方案之间的比较数据的情况来构建排名的置信度集。关键思想是，如果一个替代项（例如A）的排名高于某个其他替代项（例如B），那么很自然地假设得出一个观察结果，其中A与B处于有利位置比相反的可能性更大。这提供了一种见解，我们可以通过将其转化为测试矩不等式的问题来测试特定排名，并且可以通过反转矩不等式的这些测试来获得排名的置信度集。我们将提出的方法应用于有关日本日本职业棒球联盟各球队排名的统计推断。