标题： 基于多变量数据的尾部指数估计 显示英文标题

标题： On Tail Index Estimation based on Multivariate Data

摘要： 本文致力于研究基于独立同分布的多元观测数据的尾部指数估计问题，这些观测数据是从标准重尾分布中抽取的，即其一维Pareto类边缘分布共享相同的尾部指数。 在较弱的条件下，建立了一个随机向量的多元中心极限定理，该随机向量的分量对应于公共形状参数α的（可能是相关的）Hill估计量。 受极值空间数据分析的启发，我们引入了尾部指数为α的标准重尾随机场的概念，并展示了如何通过适当的凸线性组合坐标来构建尾部指数α的小渐近均方误差估计量。 除了渐近结果外，还通过模拟实验展示了所推广方法的相关性。 显示英文摘要

摘要： This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, i.e. of which 1-d Pareto-like marginals share the same tail index. A multivariate Central Limit Theorem for a random vector, whose components correspond to (possibly dependent) Hill estimators of the common shape index alpha, is established under mild conditions. Motivated by the statistical analysis of extremal spatial data in particular, we introduce the concept of (standard) heavy-tailed random field of tail index alpha and show how this limit result can be used in order to build an estimator of alpha with small asymptotic mean squared error, through a proper convex linear combination of the coordinates. Beyond asymptotic results, simulation experiments illustrating the relevance of the approach promoted are also presented.