Toward efficient maximum likelihood algorithms
Tae-sung Shin · 1998
Motivated by recent extensive studies of maximum likelihood (ML) algorithms, especially EM-type schemes, the author proposes 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. In the first part of this dissertation, the author illustrates the application of this algorithm to several examples--random effects model, variance components, normal finite mixture, t-distribution model, contingency table, and compares the performance of each to conventional EM-type algorithms using numerical studies. For the rest of this dissertation, new models emphasizing variance components model, which might be helpful in a data analysis, are studied and new GCM algorithms for those ML estimations are developed.