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

Author

Listed:
  • Jianling Wang

    (School of Mathematics, Shandong University, Jinan 250100, China
    Research Center for Mathematics and Interdisciplinary Sciences, Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Shandong University, Qingdao 266237, China)

  • Yihui Luan

    (Research Center for Mathematics and Interdisciplinary Sciences, Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Shandong University, Qingdao 266237, China)

  • Jiming Jiang

    (Department of Statistics, University of California, Davis, CA 95616, USA)

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 σ 2 using the method of moments; we also assess the empirical performance. Finally, three real-data examples are considered.

Suggested Citation

  • Jianling Wang & Yihui Luan & Jiming Jiang, 2022. "A Two-Step Method of Estimation for Non-Linear Mixed-Effects Models," Mathematics, MDPI, vol. 10(23), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4547-:d:990274
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