Maximum Likelihood Estimation of Linear Models for Longitudinal Data with Inequality Constraints

Abstract

Maximum likelihood (ML) estimation for linear models with longitudinal data under inequality restrictions is investigated. Within-subject correlations are modeled by parametric structure. Asymptotic properties of constrained ML estimates, including strong consistency, approximate representation and asymptotic distribution, are derived. Finally, the ML estimators with and without constraints are compared in terms of sample bias, sample mean-square error MSE and sample variance of the estimators by a simulation.

Keywords:

• Approximate representation
• Asymptotic distribution
• Inequality constraints
• Longitudinal data

Mathematics Subject Classification:

• 62H15
• 62H12
• 62F30
• 62F35

Acknowledgment

Jing Xu is supported by NSFC Project # 10671089 and SRFDP No.20060254006.

Notes

CML=ML estimator with inequality-constraints; MLE=ML estimator without inequality-constraints.