标题： 高维数据中极值方向数量的信息准则 显示英文标题

标题： Information criteria for the number of directions of extremes in high-dimensional data

摘要： 在多元极端值分析中，估计极端情况下的依赖结构具有挑战性，尤其是在高维数据的背景下。因此，一种常见的方法是通过仅考虑极端值出现的方向来降低模型维度。在本文中，我们使用Meyer和Wintenberger（2021）最近引入的稀疏正则变化概念，推导出用于确定极端事件发生方向数量的信息准则，如贝叶斯信息准则（BIC）、基于均方误差的信息准则（MSEIC）以及基于高斯似然函数的准Akaike信息准则（QAIC）。如同在极端值分析中通常的情况一样，一个具有挑战性的任务是选择用于估计的$k_n$个观测值的数量。因此，对于所有信息准则，我们提出了一种两步程序来估计极端方向的数量和$k_n$的最优选择。我们证明了Meyer和Wintenberger（2023）的AIC和MSEIC对于极端方向数量是不一致的信息准则，而BIC和QAIC是一致的信息准则。最后，在模拟研究中比较了不同信息准则的性能，并将其应用于风速数据。 显示英文摘要

摘要： In multivariate extreme value analysis, the estimation of the dependence structure in extremes is demanding, especially in the context of high-dimensional data. Therefore, a common approach is to reduce the model dimension by considering only the directions in which extreme values occur. In this paper, we use the concept of sparse regular variation recently introduced by Meyer and Wintenberger (2021) to derive information criteria for the number of directions in which extreme events occur, such as a Bayesian information criterion (BIC), a mean-squared error-based information criterion (MSEIC), and a quasi-Akaike information criterion (QAIC) based on the Gaussian likelihood function. As is typical in extreme value analysis, a challenging task is the choice of the number $k_n$ of observations used for the estimation. Therefore, for all information criteria, we present a two-step procedure to estimate both the number of directions of extremes and an optimal choice of $k_n$. We prove that the AIC of Meyer and Wintenberger (2023) and the MSEIC are inconsistent information criteria for the number of extreme directions whereas the BIC and the QAIC are consistent information criteria. Finally, the performance of the different information criteria is compared in a simulation study and applied on wind speed data.