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Asymptotic properties of nonlinear mixed-effects models. (English) Zbl 0897.62067

Gregoire, Timothy G. (ed.) et al., Modelling longitudinal and spatially correlated data: methods, applications, and future directions. Proceedings of the conference, Nantucket, USA, October 1996. New York: Springer. Lect. Notes Stat., Springer-Verlag. 122, 49-62 (1997).
Summary: The asymptotic properties of four estimators for nonlinear mixed-effects models are investigated: maximum likelihood estimator (MLE), an estimator based on the first-order approximation to the expectation function, the two-stage, and the Lindstrom-Bates estimators [M. J. Lindstrom and D. M. Bates, Biometrics 46, 673-687 (1990)]. Two asymptotic situations are considered: (i) when \(N\to \infty\) and \(n_i\) is finite and (ii) \(N\to\infty\) and \(\min n_i\to \infty\), where \(N\) is the number of individuals and \(n_i\) is the number of observations on the \(i\)th individual. For a simple one-parameter balanced exponential model only the MLE is consistent when the numbers of observations per individual, \(\{n_i\}\), are finite. The estimator based on the first-order approximation is always inconsistent, i.e., has a systematic bias. The asymptotic bias for the other three estimators is evaluated when \(N\to\infty\) and \(n_i=\text{const}\). When \(N\to\infty\) and \(\min n_i\to\infty\), the MLE, Lindstrom-Bates and two-stage estimators are equivalent. The bias for the two-stage estimator based on a second-order approximation is evaluated for the general nonlinear mixed-effects model, and a bias-corrected version of this estimator is proposed.
For the entire collection see [Zbl 0868.00060].

MSC:

62J02 General nonlinear regression
62H12 Estimation in multivariate analysis
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