A generalized Mallows model based on ϕ-divergence measures

Maria Kateri and Nikolay I. Nikolov

Journal of Multivariate Analysis, 2022, vol. 190, issue C

Abstract: Rankings occur when a set of items is ordered in agreement with some criteria or personal opinions and can be found in various problems ranging from voting and elections to food preferences. Distances on permutations are commonly used in rank data analysis and are an efficient tool for constructing probability models for rankings. In this paper, we consider the optimal property of the distance-based Mallows model in terms of the Kullback–Leibler divergence and propose a generalization based on the ϕ-divergence. In the sequel, we focus on a special parametric family of models induced by the Cressie–Read power divergence. For the suggested models, we provide parameter estimating algorithms and model fitting methods. Furthermore, we propose a simple approach for the specification of the consensus ranking, based on modal complete or partial rankings modal rankings, that could be used alternatively to complete search algorithms. As an illustration, the described procedures are applied to three examples of rank data.

Keywords: Consensus ranking; Cressie–Read power divergence; Distance-based probability models; Distances on permutations; Scale invariant statistics (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.jmva.2022.104958

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