  We present new results for consistency of maximum likelihood estimators with
a focus on multivariate mixed models. Our theory builds on the idea of using
subsets of the full data to establish consistency of estimators based on the
full data. It requires neither that the data consist of independent
observations, nor that the observations can be modeled as a stationary
stochastic process. Compared to existing asymptotic theory using the idea of
subsets we substantially weaken the assumptions, bringing them closer to what
suffices in classical settings. We apply our theory in two multivariate mixed
models for which it was unknown whether maximum likelihood estimators are
consistent. The models we consider have non-stochastic predictors and
multivariate responses which are possibly mixed-type (some discrete and some
continuous).
