4.6 Article

A General Pairwise Comparison Model for Extremely Sparse Networks

出版社

TAYLOR & FRANCIS INC
DOI: 10.1080/01621459.2022.2053137

关键词

Entry-wise error; Graph topology; Maximum likelihood estimation; Sparsity; Uniform consistency

资金

  1. Hong Kong Research Grants Council [16302881, 14301821]
  2. Direct Grants for Research, The Chinese University of Hong Kong

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This article proposes a general framework to model the mutual interactions in a network and shows that the maximum likelihood estimator is consistent under certain conditions. The analysis also reveals an important connection between graph topology and model consistency.
Statistical estimation using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this article, we propose a general framework to model the mutual interactions in a network, which enjoys ample flexibility in terms of model parameterization. Under this setup, we show that the maximum likelihood estimator for the latent score vector of the subjects is uniformly consistent under a near-minimal condition on network sparsity. This condition is sharp in terms of the leading order asymptotics describing the sparsity. Our analysis uses a novel chaining technique and illustrates an important connection between graph topology and model consistency. Our results guarantee that the maximum likelihood estimator is justified for estimation in large-scale pairwise comparison networks where data are asymptotically deficient. Simulation studies are provided in support of our theoretical findings. Supplementary materials for this article are available online.

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