On the validity of bootstrap uncertainty estimates in the Mallows-Binomial model

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.