Open Access
April 2016 Estimation in exponential families on permutations
Sumit Mukherjee
Ann. Statist. 44(2): 853-875 (April 2016). DOI: 10.1214/15-AOS1389


Asymptotics of the normalizing constant are computed for a class of one parameter exponential families on permutations which include Mallows models 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 the flexibility of the tools of this paper.


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Sumit Mukherjee. "Estimation in exponential families on permutations." Ann. Statist. 44 (2) 853 - 875, April 2016.


Received: 1 May 2015; Revised: 1 September 2015; Published: April 2016
First available in Project Euclid: 17 March 2016

zbMATH: 1341.62083
MathSciNet: MR3476619
Digital Object Identifier: 10.1214/15-AOS1389

Primary: 60F10 , 62F12
Secondary: 05A05

Keywords: Mallows model , normalizing constant , permutation , pseudo-likelihood

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 2 • April 2016
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