Consistent maximum likelihood estimation using subsets with applications to multivariate mixed models

Karl Oskar Ekvall, Galin L. Jones

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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 nonstochastic predictors and multivariate responses which are possibly mixed-type (some discrete and some continuous).

Original languageEnglish (US)
Pages (from-to)932-952
Number of pages21
JournalAnnals of Statistics
Volume48
Issue number2
DOIs
StatePublished - 2020

Keywords

  • Consistency
  • Crossed random effects
  • GLMM
  • Maximum likelihood
  • MGLMM
  • Subset argument

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