Ajuste de cópulas bivariadas via marginal na diagonal e teste para dependência de valores extremos via ajuste de função de Pickands por polinômios de Bernstein

Abstract

Studies about goodness of fit for copula and tests to verify the dependence of extreme values are of great interest in statistic and it are relevant in other areas such as the economy. This thesis approaches these two issues and it is presented in three chapters. The first chapter takes care of the theoretical framework that it includes measures of association for posts, copula and dependence of extreme values; the second proposes two new tests about verification to goodness of fit for bivariate copula, and it based on marginal in principal and secondary diagonals; the third proposes a method to verify that a given set of bivariate data has dependency of extreme value, by nonparametric estimating of the Pickands function and it based on Bernstein polynomial optimization.