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 (theta) over tilde of the vector theta of parameters is obtained by solving estimation equations, with a working covariance matrix as the identity matrix. It is shown that (theta) over tilde is consistent. If, furthermore, we have an estimated covariance matrix, (V) over cap, by (theta) over tilde, a second-step estimator B can be obtained by solving the optimal estimation equations. It is shown that maintains asymptotic optimality. We establish the consistency and asymptotic normality of the proposed estimators. Simulation results show the improvement of (theta) over cap over (theta) over tilde. Furthermore, we provide a method to estimate the variance sigma(2) using the method of moments; we also assess the empirical performance. Finally, three real-data examples are considered.

Automated summary

The main goal of this paper is to propose a two-step method for the estimation of parameters in non-linear mixed-effects models. It is shown that the proposed method is consistent and asymptotically normal, with improved performance compared to previous methods. The paper also presents a method for estimating the variance and evaluates its empirical performance. Three real-data examples are considered for validation.