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arXiv · 1307.0978

Estimation in exponential families on permutations

Sumit Mukherjee
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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.

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Sumit Mukherjee. 2015-05-13. Estimation in exponential families on permutations. https://doi.org/10.1214/15-aos1389

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