Statistical Depth Functions for Ranking Distributions: Definitions, Statistical Learning and Applications. (arXiv:2201.08105v1 [cs.LG])

The concept of median/consensus has been widely investigated in order to
provide a statistical summary of ranking data, i.e. realizations of a random
permutation $\Sigma$ of a finite set, $\{1,\; \ldots,\; n\}$ with $n\geq 1$
say. As it sheds light onto only one aspect of $\Sigma$'s distribution $P$, it
may neglect other informative features. It is the purpose of this paper to
define analogs of quantiles, ranks and statistical procedures based on such
quantities for the analysis of ranking data …

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