Goodness-of-fit tests for archimedean copula models

In this paper, we propose two tests for parametric models belonging to the Archimedean copula family, one for uncensored bivariate data and the other one for right-censored bivariate data. Our test procedures are based on the Fisher transform of the correlation coefficient of a bivariate (U, V), which is a one-toone transform of the original random pair (T₁,T₂) that can be modeled by an Archimedean copula model. A multiple imputation technique is applied to establish our test for censored data and its p value is computed by combining test statistics obtained from multiply imputed data sets. Simulation studies suggest that both procedures perform well when the sample size is large. The test for censored data is carried out for a medical data example.