Estimation in exponential families on permutations

Sumit Mukherjee
2016 Annals of Statistics  
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
more » ... l with Kendall's Tau is also analyzed to demonstrate flexibility of the tools of this paper.
doi:10.1214/15-aos1389 fatcat:ycsflxywcfefxhxcbbdmrkicpq