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

Jianling Wang, Yihui Luan and Jiming Jiang ()
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Jianling Wang: School of Mathematics, Shandong University, Jinan 250100, 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

Mathematics, 2022, vol. 10, issue 23, 1-18

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.

Keywords: two-step estimate; consistency; estimation equation; non-linear mixed model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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