Abstract: We considered the convergence of EMS algorithm. Firstly, we gave a necessary condition for the minimum point of observed generalized information criterion (GIC). Secondly, under the conditions of finiteness of model space, compactness of parameter space, continuity of Q function, we proved that it was necessary for the limit points of the sequence generated by EMS algorithm to satisfy the minimum points of observed GIC, which was a supplement to the global convergence of EMS algorithm. Thirdly, we gave an example of Gaussian graphical model which satisfied the necessary condition, but did not satisfy conditions for global convergence. Finally, we proved the global convergence of E-MS algorithm.

Key words: missing data, model selection, observed GIC, E-MS algorithm