论文标题
对本福德定律的严格测试
Severe testing of Benford's law
论文作者
论文摘要
本福德定律通常被用作支持与数据质量或数据操纵甚至欺诈有关的关键决策的支持。但是，许多作者认为，即使在这种应用中的典型尺寸样本中应用，传统的统计测试将拒绝数据“本福德 - 性”的零，即使在与本福德定律的微小且实际上并不重要的情况下。因此，他们建议使用替代标准，但是缺乏坚实的统计基础。本文在本福德法律测试的背景下，有助于关于“大$ n $”（或“多余功率”）问题的辩论。讨论了有关适合测试良好性的严重性测试概念的讨论，并特别关注与本福德定律一致的测试。为此，我们还得出了平均绝对偏差（$ MAD $）统计量以及渐近标准正常测试的渐近分布。最后，将严重性测试原则应用于有争议的六个有争议的数据集，以评估其“ Benford-ness”。
Benford's law is often used as a support to critical decisions related to data quality or the presence of data manipulations or even fraud. However, many authors argue that conventional statistical tests will reject the null of data "Benford-ness" if applied in samples of the typical size in this kind of applications, even in the presence of tiny and practically unimportant deviations from Benford's law. Therefore, they suggest using alternative criteria that, however, lack solid statistical foundations. This paper contributes to the debate on the "large $n$" (or "excess power") problem in the context of Benford's law testing. This issue is discussed in relation with the notion of severity testing for goodness of fit tests, with a specific focus on tests for conformity with Benford's law. To do so, we also derive the asymptotic distribution of the mean absolute deviation ($MAD$) statistic as well as an asymptotic standard normal test. Finally, the severity testing principle is applied to six controversial data sets to assess their "Benford-ness".
