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Monge–Kantorovich 深度、分位数、秩与符号AI 解读

We propose new concepts of statistical depth, multivariate quantiles, vector quantiles and ranks, ranks and signs, based on canonical transportation maps between a distribution of interest on $\mathbb{R}^{d}$ and a reference distribution on the $d$-dimensional unit ball. The new depth concept, called Monge–Kantorovich depth, specializes to halfspace depth for $d=1$ and in the case of spherical distributions, but for more general distributions, differs from the latter in the…

部分识别的不完备结构模型推断的组合方法AI 解读

We propose a computationally feasible inference method in finite games of complete information. Galichon and Henry, 2011 and Beresteanu, Molchanov, and Molinari, 2011 show that the empirical content in such models is characterized by a collection of moment inequalities whose number increases exponentially with the number of discrete outcomes. We propose an equivalent characterization based on classical combinatorial optimization methods that allows the construction of…

欧氏显示偏好：空间投票模型的检验AI 解读

SUMMARY In the spatial model of voting, voters choose the candidate closest to them in the ideological space. Recent work by Degan and Merlo in 2009 shows that it is falsifiable on the basis of individual voting data in multiple elections. We show how to tackle the fact that the model only partially identifies the distribution of voting profiles and we give a formal revealed preference test of the spatial voting model in three national elections in the USA, and strongly…