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

Consistent Maximum Likelihood Estimation Using Subsets with Applications to Multivariate Mixed Models