Motivated by recent extensive studies of maximum likelihood (ML) algorithms, especially EM-type schemes, we propose a class of generalized conditional maximization (GCM) algorithms that pursues dimension reduction as well as stability of algorithm simultaneously. This model-dependent approach for developing ML algorithms is to apply an appropriate, but possibly different approximation to each selected subset of parameters that ensure fast and stable convergence to a candidate for a local maximum. We illustrate the application of this algorithm to several examples - random effects model, variance components, normal finite mixture, t-distribution model, contingency table, and compare the performance of each to conventional EM-type algorithms using numerical studies.

Keywords and Phrases:  Iterative methods, rate of convergence, monotone convergence, global convergence, generalized EM, successive overrelazation, acceleration, Gauss-Seidel, Jacobi

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