The extremal dependence structure of a regularly varying random vector Xis fully described by its limiting spectral measure. In this paper, we investigate how torecover characteristics of the measure, such as extremal coefficients, from the extremalbehaviour of convex combinations of components of X. Our considerations result in aclass of new estimators of moments of the corresponding combinations for the spectralvector. We show asymptotic normality by means of a functional limit theorem and, focusingon the estimation of extremal coefficients, we verify that the minimal asymptoticvariance can be achieved by a plug-in estimator using subsampling bootstrap. We illustratethe benefits of our approach on simulated and real data.

翻译：正则变化随机向量X的极值依赖结构完全由其极限谱测度所刻画。本文研究如何从X分量凸组合的极值行为中恢复该测度的特征，例如极值系数。我们的推导得到了一类新的谱向量对应组合矩的估计量。通过函数极限定理，我们证明了估计量的渐近正态性，并聚焦于极值系数估计，验证了使用子抽样自助法的插件估计量可以达到最小渐近方差。我们在模拟数据和真实数据上展示了该方法的优势。