Total positivity in multivariate extremes
研究了多元极值中的正相关性，提出EMTP2概念，证明Hüsler-Reiss分布满足EMTP2当且仅当其精度矩阵为连通图的拉普拉斯矩阵，并给出带拉普拉斯约束的凸优化估计方法，在多瑙河流量数据中表现优于现有方法。
Positive dependence is present in many real world data sets and has appealing stochastic properties that can be exploited in statistical modeling and in estimation. In particular, the notion of multivariate total positivity of order 2 (MTP2) is a convex constraint and acts as an implicit regularizer in the Gaussian case. We study positive dependence in multivariate extremes and introduce EMTP2, an extremal version of MTP2. This notion turns out to appear prominently in extremes, and in fact, it is satisfied by many classical models. For a Hüsler–Reiss distribution, the analogue of a Gaussian distribution in extremes, we show that it is EMTP2 if and only if its precision matrix is a Laplacian of a connected graph. We propose an estimator for the parameters of the Hüsler–Reiss distribution under EMTP2 as the solution of a convex optimization problem with Laplacian constraint. We prove that this estimator is consistent and typically yields a sparse model with possibly nondecomposable extremal graphical structure. Applying our methods to a data set of Danube River flows, we illustrate this regularization and the superior performance compared to existing methods.