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Mathematics > Statistics Theory

arXiv:2206.12365 (math)
[Submitted on 24 Jun 2022 (v1), last revised 20 Jul 2022 (this version, v2)]

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

Authors:Michael Pearce, Elena A. Erosheva
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Abstract: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.
Comments: 9 pages
Subjects: Statistics Theory (math.ST)
Cite as: arXiv:2206.12365 [math.ST]
  (or arXiv:2206.12365v2 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.2206.12365

Submission history

From: Michael Pearce [view email]
[v1] Fri, 24 Jun 2022 16:30:19 UTC (24 KB)
[v2] Wed, 20 Jul 2022 18:07:29 UTC (24 KB)
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