Statistical Analysis for Nonlinear Mixed Models with Random Design

In this paper, we study point estimation and confidence interval construction for the parameters of interest in nonlinear mixed effects models with random times of repeated measurements for subjects. Under only moment conditions, we define the moment estimators of the fixed effects, the covariance matrix of the random effects and the variance of the errors. The consistency and asymptotic normality of the estimators are obtained. To construct confidence intervals of the variances of the error and the random effects, we also estimate the fourth moments of the random effects and the errors. For illustrating the effect of our method, a simulation study is given.