Improved EM for Mixture Proportions with Applications to Nonparametric ML Estimation for Censored Data

Improved EM strategies, based on the idea of efficient data augmentation (Meng and van Dyk 1997, 1998), are presented for ML estimation of mixture proportions. The resulting algorithms inherit the simplicity, ease of implementation, and monotonic convergence properties of EM, but have considerably improved speed. Because conventional EM tends to be slow when there exists a large overlap between the mixture components, we can improve the speed without sacrificing the simplicity or stability, if we can reformulate the problem so as to reduce the amount of overlap. We propose simple "squeezing" strategies for that purpose. Moreover, for high-dimensional problems, such as computing the nonparametric MLE of the distribution function with censored data, a natural and effective remedy for conventional EM is to add exchange steps (based on improved EM) between adjacent mixture components, where the overlap is most severe. Theoretical considerations show that the resulting EM-type algorithms, when carefully implemented, are globally convergent. Simulated and real data examples show dramatic improvement in speed in realistic situations.