Sankhya: The Indian Journal of Statistics

2005, Volume 67, Pt. 4, 736--763

Strong Consistency of MLE in Nonlinear Mixed-effects Models with Large Cluster Size

Lei Nie, Georgetown University, Washington, USA
Min Yang, University of Missouri-Columbia, Columbia, USA

SUMMARY. The search for conditions for the consistency of maximum likelihood estimators in nonlinear mixed effects models is difficult due to the fact that, in general, the likelihood can only be expressed as an integral over the random effects. For repeated measurements or clustered data, we focus on  asymptotic theory for the maximum likelihood estimator for the case where the cluster sizes go to infinity, which is a minimum assumption required to validate most of the available methods of inference in nonlinear mixed-effects models. In particular, we establish sufficient conditions for the (strong) consistency of the maximum likelihood estimator of the fixed effects. Our results extend the results of Jennrich (1969) and Wu (1981) for nonlinear fixed-effects models to  nonlinear mixed-effects models.

AMS (2000) subject classification. 62J05, 62F12.

Key words and phrases. Maximum likelihood estimator (MLE), nonlinear models, random effects, strong consistency.

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