The COPULA Procedure

Exact Maximum Likelihood Estimation (MLE)

Suppose that the marginal distributions of vector elements $\pmb x_ i = ( x_{i1}, x_{i2}, \ldots , x_{im} )^\top $, $i=1,\ldots ,n$ are already known to be uniform. Then the parameter $\theta $ is estimated by exact maximum likelihood:

\[ \hat{\theta } = \arg \max _{{\theta }\in {\Theta }} \sum _{i=1}^{n} \log c(x_{i1}, x_{i2}, \ldots , x_{im}; {\theta }) \]