CONSISTENT MAXIMUM LIKELIHOOD ESTIMATION USING SUBSETS WITH APPLICATIONS TO MULTIVARIATE MIXED MODELS

• 成果类型: Article
• 署名作者: Ekvall, Karl Oskar; Jones, Galin L.
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1830
• 发表日期: 2020
• 页码: 932-952
• 关键词: asymptotic properties

摘要

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).