Estimation bayésienne d'une fonction de Pickands par des splines cubiques
The subject of our thesis is intersection between two fields: The Extreme Value Theory (EVT) and copulas. The object of EVT is to find the limit law of the maximum of a sample. Due to the results of EVT, we can model extreme phenomena. In addition, there is a bivariate variant of EVT. The bivariate variant of EVT uses a family of copulas called extreme value copulas to account for the connection between the two extreme events. Any copula with extreme values depends on a Pickands function. The object of our thesis is to estimate the Pickands function from data. We have found a way to build a Pickands function using cubic splines. From this construction, we obtain an extended family of Pickands functions in which we perform our statistical inference. We chose the Bayesian approach to build the estimator and the MCMC methods for the estimates. The method was applied on simulated and real data.
MCMC Extrem value copulas Pickands Function