The stable tail dependence function provides a full characterization of the extremal dependence structures. Unfortunately, the estimation of the stable tail dependence function often suffers from significant bias, whose scale relates to the Peaks-Over-Threshold (POT) second-order parameter. For this second-order parameter, this paper introduces a penalized estimator that discourages it from being too close to zero. This paper then establishes this estimator's asymptotic consistency, uses it to correct the bias in the estimation of the stable tail dependence function, and illustrates its desirable empirical properties in the estimation of the extremal dependence structures.

翻译：稳定的尾部依赖性功能为极端依赖性结构提供了全面的特征描述。 不幸的是,对稳定的尾部依赖性功能的估计往往存在重大偏差,其规模与峰值对硫码头的二级参数有关。 对于这个第二阶参数,本文引入了一种惩罚性的估测符,劝阻它不要太接近于零。本文随后确定了这个估测符的无症状一致性,用它来纠正对稳定的尾部依赖性功能的估计偏差,并说明了它在估计极端依赖性结构时的适当经验属性。