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Two goodness-of-fit tests for copulas are being investigated. The first onedeals with the case of elliptical copulas and the second one deals withindependent copulas. These tests result from the expansion of the projectionpursuit methodology we will introduce in the present article. This methodenables us to determine on which axis system these copulas lie as well as theexact value of these very copulas in the basis formed by the axes previouslydetermined irrespective of their value in their canonical basis. Simulationsare also presented as well as an application to real datasets.

Goodness-of-fit Tests For Elliptical And Independent Copulas Through Projection Pursuit