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最优传输定义的多元秩与分位数：一致性、速率和非参数检验AI 解读

In this paper, we study multivariate ranks and quantiles, defined using the theory of optimal transport, and build on the work of Chernozhukov et al. (Ann. Statist. 45 (2017) 223–256) and Hallin et al. (Ann. Statist. 49 (2021) 1139–1165). We study the characterization, computation and properties of the multivariate rank and quantile functions and their empirical counterparts. We derive the uniform consistency of these empirical estimates to their population versions, under…

Ising 模型参数的联合估计AI 解读

We study joint estimation of the inverse temperature and magnetization parameters $(\beta ,B)$ of an Ising model with a nonnegative coupling matrix $A_{n}$ of size $n\times n$, given one sample from the Ising model. We give a general bound on the rate of consistency of the bi-variate pseudo-likelihood estimator. Using this, we show that estimation at rate $n^{-1/2}$ is always possible if $A_{n}$ is the adjacency matrix of a bounded degree graph. If $A_{n}$ is the scaled…