Fisher scoring: An interpolation family and its Monte Carlo implementations

The Fisher scoring method is widely used for likelihood maximization, but its application can be difficult in situations where the expected information matrix is not available in closed form or when parameters have constraints. In this paper, we describe an interpolation family that generalizes the Fisher scoring method and propose a general Monte Carlo approach that makes these generalized methods also applicable in such situations. With this approach, random samples are generated from the iteratively estimated models and used to provide estimates of the expected information. As a result, the likelihood function can be optimized by repeatedly solving weighted linear regression problems. Specific extensions of this general approach to fitting multivariate normal mixtures and to fitting mixed-effects models with a single discrete random effect are also described. Numerical studies show that the proposed algorithms are fast and reliable to use, as compared with the classical expectation-maximization algorithm.