A new algorithm for estimating the parameters and their asymptotic covariance in correlation and association models

In this paper, an algorithm providing Maximum Likelihood estimates and their asymptotic covariance matrix for the parameters in correlation models and association models is proposed. It is based on a Fisher's scoring type algorithm using the asymptotic covariance matrix of Maximum Likelihood estimates whose expression is also given. The convergence of the proposed algorithm is generally quickly obtained, even for large contingency tables, as illustrated through 2 examples.