Abstract
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 σ2 using the method of moments; we also assess the empirical performance. Finally, three real-data examples are considered.
Funder
National Key R&D Program of China
National Science Foundation of China
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference21 articles.
1. FDA US (1999). Guidance for Industry: Population Pharmacokinetics, FDA.
2. Fan, J., and Koul, H. (2006). Frontiers of Statistics in Honor of Professor Peter J. Bickel’s 65th Birthday, Imperial College Press.
3. Gelman, A., Carlin, J., Stern, H., and Rubin, D. (2004). Bayesian Data Analysis, Chapman & Hall/CRC. [2nd ed.].
4. Nonlinear mixed effects models for repeated measures data;Lindstrom;Biometrics,1990
5. Approximations to the Log-likelihood function in Nonlinear Mixed Effects Models;Pinheiro;J. Comput. Graph. Stat.,1995