Estimation in exponential families on permutations

Abstract

Asymptotics of the normalizing constant is computed for a class of one parameter exponential families on permutations which includes Mallows model with Spearmans's Footrule and Spearman's Rank Correlation Statistic. The MLE, and a computable approximation of the MLE are shown to be consistent. The pseudo-likelihood estimator of Besag is shown to be $\sqrt{n}$-consistent. An iterative algorithm (IPFP) is proved to converge to the limiting normalizing constant. The Mallows model with Kendall's Tau is also analyzed to demonstrate flexibility of the tools of this paper.

The presentation of the paper is changed. Proof of consistency of MLE and an approximation to the MLE is included. The convergence of the discrete IPFP algorithm is analyzed as opposed to the continuous version

References in corpus (4)

• Multivariate Archimedean copulas, $d$-monotone functions and ${\ell }_1$-norm symmetric distributions
• Thermodynamic Limit for the Mallows Model on $S_n$
• Content Modeling Using Latent Permutations
• Estimation and Clustering with Infinite Rankings

Cited by in corpus (5)

• Fixed points and cycle structure of random permutations
• Antithetic and Monte Carlo kernel estimators for partial rankings
• Optimal Permutation Recovery in Permuted Monotone Matrix Model
• A central limit theorem for descents of a Mallows permutation and its inverse
• Sequential Rank and Preference Learning with the Bayesian Mallows Model