Title: Hypothesis testing for tail dependence parameters on the boundary of the parameter space
Authors: Anna Kiriliouk - University of Namur (Belgium) [presenting]
Abstract: 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 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 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.