Maximum likelihood estimation- practical merits of variable metric optimisation methods.

The Davidon- Fletcher- Powell optimisation procedure is proposed as a method to be employed in Maximum Likelihood Estimation. It has the advantage of enabling the variance- covariance matrix of the estimates to be computed without the need to evaluate second derivatives of the log- likelihood function, or to invert the matrix of these derivatives. Examples of the successful application of this idea to parametric model fitting of reliability data, as well as applications to the proportional hazards model are given.