On fast computation of the non-parametric maximum likelihood estimate of a mixing distribution

A fast algorithm for computing the non-parametric maximum likelihood estimate of a mixing distribution is presented. At each iteration, the algorithm adds new important points to the support set as guided by the gradient function, updates all mixing proportions via a quadratically convergent method and discards redundant support points straightaway. With its convergence being theoretically established, numerical studies show that it is very fast and stable, compared with several other algorithms that are available in the literature. Copyright 2007 Royal Statistical Society.