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A comparison of dependence function estimators in multivariate extremes

机译：多元极值中依赖函数估计量的比较

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摘要

Various nonparametric and parametric estimators of extremal dependence have been proposed in the literature. Nonparametric methods commonly suffer from the curse of dimensionality and have been mostly implemented in extreme-value studies up to three dimensions, whereas parametric models can tackle higher-dimensional settings. In this paper, we assess, through a vast and systematic simulation study, the performance of classical and recently proposed estimators in multivariate settings. In particular, we first investigate the performance of nonparametric methods and then compare them with classical parametric approaches under symmetric and asymmetric dependence structures within the commonly used logistic family. We also explore two different ways to make nonparametric estimators satisfy the necessary dependence function shape constraints, finding a general improvement in estimator performance either (i) by substituting the estimator with its greatest convex minorant, developing a computational tool to implement this method for dimensions or (ii) by projecting the estimator onto a subspace of dependence functions satisfying such constraints and taking advantage of Bernstein-B,zier polynomials. Implementing the convex minorant method leads to better estimator performance as the dimensionality increases.
机译：文献中已经提出了各种极端依赖的非参数和参数估计器。非参数方法通常会遭受维度的诅咒，并且大多数已在多达三个维度的极值研究中实现，而参数模型可以解决更高维度的设置。在本文中，我们通过大量系统的模拟研究评估了多元估计中经典估计器和最近提出的估计器的性能。特别是，我们首先研究非参数方法的性能，然后将它们与经典逻辑方法在常用逻辑族内的对称和非对称依赖结构下进行比较。我们还探索了两种不同的方法来使非参数估计器满足必要的依赖函数形状约束，或者通过以下方法找到估计器性能的总体改进：（i）用最大凸次要量代替估计器，开发一种计算工具来实现该方法的尺寸或（ii）通过将估计量投影到满足此类约束的依赖函数的子空间上，并利用Bernstein-B，zier多项式。随着维数的增加，实施凸次要方法会导致更好的估计器性能。

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