Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. The max-linear model is a parametric tail dependence model which is dense in the class of multivariate extreme-value models. Being non-differentiable, it cannot be estimated using likelihood-based methods, so that minimum distance estimation forms a valuable alternative. Currently, estimation is limited to the set-up where the number of factors and/or the structure of the model is defined a priori, because answering these questions necessitates estimation and testing at the boundary of the parameter space. The main goal of this paper is to propose hypothesis tests for tail dependence parameters that, under the null hypothesis, are on the boundary of the alternative hypothesis. We give the asymptotic distribution of the weighted least squares estimator proposed in Einmahl, Kiriliouk and Segers (2017, to be published in Extremes) when the true parameter is on the boundary of the parameter space, and we propose two test statistics whose asymptotic distribution is easily computable. An extensive simulation study evaluates the performance of the test statistics, which are then applied to the stock market prices of two NYSE companies.

中文翻译：

---

参数空间边界上的尾部依赖参数的假设检验

建模多元尾部依赖关系是极值理论中的关键挑战之一。最大线性模型是参数尾部依赖模型，在多变量极值模型的类别中比较密集。由于是不可微的，因此无法使用基于似然的方法进行估算，因此最小距离估算将形成有价值的选择。当前，估计仅限于先验定义因素数量和/或模型结构的设置，因为要回答这些问题，就必须在参数空间的边界进行估计和测试。本文的主要目的是提出针对尾部依赖参数的假设检验，这些假设在原假设下位于备选假设的边界上。当真实参数在参数空间的边界上时，我们给出了Einmahl，Kiriuliuk和Segers（2017年将在Extremes中发布）中提出的加权最小二乘估计量的渐近分布，并且我们提出了两个检验统计量，其渐近分布为容易计算。广泛的模拟研究评估了测试统计数据的性能，然后将其应用于两家纽约证券交易所公司的股票市场价格。