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Title: Asymptotic theory of maximum likelihood estimators in mixed-effects models with a fixed number of clusters Authors:  ChihHao Chang - National University of Kaohsiung (Taiwan) [presenting]
Abstract: A linear mixed-effects model with clustered structure is considered, where the parameters are estimated by maximum likelihood (ML) based on possibly unbalanced data. Inference of this model is typically done based on the asymptotic theory assuming that the number of clusters tends to infinity with the sample size. However, when the number of clusters is fixed, the traditional asymptotic theory developed under a divergent number of clusters is no longer valid. We establish the asymptotic properties of the ML estimators of the random-effects parameters under a general setting, including models with fixed numbers of clusters. The asymptotic theorems allow both the fixed effects and the random effects to be misspecified, and the dimensions of both effects to go to infinity with the sample size.