  Recently, a so-called E-MS algorithm was developed for model selection in the
presence of missing data. Specifically, it performs the Expectation step (E
step) and Model Selection step (MS step) alternately to find the minimum point
of the observed generalized information criteria (GIC). In practice, it could
be numerically infeasible to perform the MS-step for high dimensional settings.
In this paper, we propose a more simple and feasible generalized EMS (GEMS)
algorithm which simply requires a decrease in the observed GIC in the MS-step
and includes the original EMS algorithm as a special case. We obtain several
numerical convergence results of the GEMS algorithm under mild conditions. We
apply the proposed GEMS algorithm to Gaussian graphical model selection and
variable selection in generalized linear models and compare it with existing
competitors via numerical experiments. We illustrate its application with three
real data sets.
