  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.
