Miscellanea On stochastic versions of the algorithm
Ian C. Marschner · Biometrika · 2001
A previously proposed stochastic modification of the algorithm is discussed, in which an intractable ‐ step is replaced by a single simulation of the complete data, followed by averaging of the resulting Markov chain iterative sequence. A connection is drawn between this approach and a modified algorithm in which the ‐ and ‐ steps are carried out in reverse order. Since this modified algorithm is equivalent to solving a biased estimating equation in finite samples, a simple modification of the stochastic algorithm is suggested. The modified stochastic algorithm is applicable when the ‐ step of an algorithm is intractable, and it is related to a deterministic algorithm that solves an unbiased estimating equation. In small‐sample simulation studies of standard censoring and mixture problems, the modified stochastic algorithm outperforms the usual stochastic algorithm and the maximum likelihood estimator. In large samples all approaches perform similarly.