Dominating Points of Gaussian Extremes
Dominating Points of Gaussian Extremes
复制标题
高斯极值的控制点
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Prateek Jaiswal
中科院分区：
文献类型：
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作者：
Harsha Honnappa;R. Pasupathy;Prateek Jaiswal
在d维欧氏空间中，对闭凸集上高斯极值统计量的大偏差进行了量化。渐近性意味着极值分布呈现出一个速率函数，该速率函数是位于凸集边界上的唯一“支配点”的简单二次函数。此外，支配点被确定为某个凸二次规划问题的优化器，表明高斯随机向量的依赖结构和凸集的几何形状在确定渐近性方面存在“勾结”。我们专门研究我们的主要结果，多面体集经常出现在其他情况下，涉及对数渐近。我们还将主要结果推广到一般凸集上高斯混合极值统计量的大偏差的刻画。我们的研究结果产生的背景下，罕见事件的概率估计和随机优化的影响，因为主导点和率函数的性质，建议重要的抽样措施。
We quantify the large deviations of Gaussian extreme value statistics on closed convex sets in d-dimensional Euclidean space. The asymptotics imply that the extreme value distribution exhibits a rate function that is a simple quadratic function of a unique "dominating point" located on the boundary of the convex set. Furthermore, the dominating point is identified as the optimizer of a certain convex quadratic programming problem, indicating a "collusion" between the dependence structure of the Gaussian random vectors and the geometry of the convex set in determining the asymptotics. We specialize our main result to polyhedral sets which appear frequently in other contexts involving logarithmic asymptotics. We also extend the main result to characterize the large deviations of Gaussian-mixture extreme value statistics on general convex sets. Our results have implications to contexts arising in rare-event probability estimation and stochastic optimization, since the nature of the dominating point and the rate function suggest importance sampling measures.