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Maximum Likelihood Estimation of the correlation parameters for elliptical copulas

We present an algorithm to obtain the maximum likelihood estimates of the correlation parameters of elliptical copulas. Previously existing methods for this task were either fast but only approximate or exact but very time-consuming, especially for high-dimensional problems. Our proposal combines the advantages of both, since it obtains the exact estimates and its performance makes it suitable for most practical applications. The algorithm is given with explicit expressions for the Gaussian and Student's t copulas.