In this paper we study a class of exponential family on permutations, which includes some of the commonly studied Mallows models. We show that the pseudo-likelihood estimator for the natural parameter in the exponential family is asymptotically normal, with an explicit variance. Using this, we are able to construct asymptotically valid confidence intervals. We also show that the MLE for the same problem is consistent everywhere, and asymptotically normal at the origin. In this special case, the asymptotic variance of the cost effective pseudo-likelihood estimator turns out to be the same as the cost prohibitive MLE. To the best of our knowledge, this is the first inference result on permutation models including Mallows models, excluding the very special case of Mallows model with Kendall's Tau.

翻译：本文研究一类排列上的指数族分布，其中包括一些常见的马洛斯模型。我们证明了该指数族中自然参数的伪似然估计量具有渐近正态性，并给出了显式方差。利用这一结果，我们能够构建渐近有效的置信区间。我们还证明，同一问题下的极大似然估计量处处相合，且在原点处具有渐近正态性。在这种特殊情况下，成本效益高的伪似然估计量的渐近方差与成本高昂的极大似然估计量相同。据我们所知，这是除肯德尔τ距离马洛斯模型这一特例之外，首次针对包含马洛斯模型的排列模型推断结果。