Despite the popularity of mixed models, it was unknown until recently whether maximum likelihood estimators are consistent even in some simple generalized linear mixed models with crossed random effects. In this talk, new results that use a non-trivial relation between the likelihood of the full data and that of a subset to establish consistency are presented. The relation allows one to formalize the intuition that estimators based on the full data should be consistent if those based on a subset are. The talk covers how subsets can be used to prove consistency of maximum likelihood estimators in mixed models, including ones with crossed random effects, but also how the argument can be extended to a much larger class of parametric models.
Personal website of Karl Oskar Ekvall