Estimation of the spectral measure from convex combinations of regularly varying random vectors
研究如何从正则变化随机向量分量的凸组合的极值行为中恢复谱测度的特征（如极值系数），提出了一类新的谱向量矩估计量，并证明其渐近正态性，通过子抽样自举实现最小渐近方差。
The extremal dependence structure of a regularly varying random vector X is fully described by its limiting spectral measure. In this paper, we investigate how to recover characteristics of the measure, such as extremal coefficients, from the extremal behaviour of convex combinations of components of X. Our considerations result in a class of new estimators of moments of the corresponding combinations for the spectral vector. We show asymptotic normality by means of a functional limit theorem and, focusing on the estimation of extremal coefficients, we verify that the minimal asymptotic variance can be achieved by a plug-in estimator using subsampling bootstrap. We illustrate the benefits of our approach on simulated and real data.