Ranking Inferences Based on the Top Choice of Multiway Comparisons
Jianqing Fan, Zhipeng Lou, Weichen Wang, Mengxin Yu

TL;DR
This paper develops a statistical framework for ranking items based on top-choice data from multiway comparisons, extending existing models, establishing convergence rates, and providing confidence intervals for scores and ranks.
Contribution
It introduces a novel inference method for multiway ranking data, including asymptotic normality results and a bootstrap-based confidence interval construction.
Findings
Established convergence rates for preference scores.
Proposed a bootstrap method for confidence intervals.
Validated methods through simulations and real data.
Abstract
This paper considers ranking inference of items based on the observed data on the top choice among randomly selected items at each trial. This is a useful modification of the Plackett-Luce model for -way ranking with only the top choice observed and is an extension of the celebrated Bradley-Terry-Luce model that corresponds to . Under a uniform sampling scheme in which any distinguished items are selected for comparisons with probability and the selected items are compared times with multinomial outcomes, we establish the statistical rates of convergence for underlying preference scores using both -norm and -norm, with the minimum sampling complexity. In addition, we establish the asymptotic normality of the maximum likelihood estimator that allows us to construct confidence intervals for the underlying scores. Furthermore, we…
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Taxonomy
TopicsEconomic and Environmental Valuation · Game Theory and Voting Systems · Statistical Methods and Bayesian Inference
