The Mallows-Binomial distribution is the first joint statistical model for rankings and ratings (Pearce and Erosheva, 2022). Because frequentist estimation of the model parameters and their uncertainty is challenging, it is natural to consider the nonparametric bootstrap. However, it is not clear that the nonparametric bootstrap is asymptotically valid in this setting. This is because the Mallows-Binomial model is parameterized by continuous quantities whose discrete order affects the likelihood. In this note, we demonstrate that bootstrap uncertainty of the maximum likelihood estimates in the Mallows-Binomial model are asymptotically valid.

翻译：Mallows-Binomial分布法是排名和评级的第一个联合统计模型(Pearce和Erosheva, 2022年)。由于对模型参数的经常估计及其不确定性具有挑战性,因此自然考虑非参数性靴子陷阱。然而,尚不清楚非参数性靴子陷阱在此环境中是否具有同等效力。这是因为 Mallows-Binomial模型的参数是连续数量,其离散顺序会影响可能性。 在本说明中,我们表明,Mallows-Binomial模型中最大可能性估计的靴子陷阱不确定性是无效的。