The constrained Fisher scoring method for maximum likelihood computation of a nonparametric mixing distribution

This paper proposes a new method for computing the nonparametric maximum likelihood estimate of a mixing distribution. It uses the Fisher scoring quadratic approximation to the log-likelihood function of the mixing proportions. At each iteration, new candidate support points are found and included, as guided by the gradient function, and bad support points are discarded, after being found redundant by optimizing the quadratic approximation. Numerical studies show that the CFS method is generally competitive with the fast and stable constrained Newton method; it may even have an advantage over the latter when the initial estimate is badly chosen.