Maximum Likelihood Estimation of the correlation parameters for elliptical copulas

TL;DR

This paper introduces an efficient algorithm for exact maximum likelihood estimation of correlation parameters in elliptical copulas, balancing accuracy and computational speed for high-dimensional problems.

Contribution

It provides a novel algorithm that achieves exact estimates of correlation parameters in elliptical copulas with improved efficiency over existing methods.

Findings

The algorithm is explicit for Gaussian and Student's t copulas.

It outperforms previous methods in speed while maintaining accuracy.

Suitable for high-dimensional applications.

Abstract

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.