A Two-Step Method of Estimation for Non-Linear Mixed-Effects Models.

The main goal of this paper is to propose a two-step method for the estimation of parameters in non-linear mixed-effects models. A first-step estimate θ ˜ of the vector θ of parameters is obtained by solving estimation equations, with a working covariance matrix as the identity matrix. It is shown that θ ˜ is consistent. If, furthermore, we have an estimated covariance matrix, V ^ , by θ ˜ , a second-step estimator θ ^ can be obtained by solving the optimal estimation equations. It is shown that θ ^ maintains asymptotic optimality. We establish the consistency and asymptotic normality of the proposed estimators. Simulation results show the improvement of θ ^ over θ ˜ . Furthermore, we provide a method to estimate the variance σ 2 using the method of moments; we also assess the empirical performance. Finally, three real-data examples are considered. [ABSTRACT FROM AUTHOR]