On quasi-Newton methods for maximum likelihood estimates with applications to the mixture density problem

A quasi-Newton algorithm with an adaptive global convergence scheme is used for numerical maximum likelihood estimates (MLE). For this method, which uses a DFP-type Hessian update for unconstrained minimization, q-superlinear local convergence is shown. We discuss this in the context of a broader class of algorithms, among them R. A. Fisher's method of scoring and the EM algorithm. A computer code, MLESOL, is described and applied to the mixture density problem.