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Some asymptotic results for semiparametric nonlinear mixed-effects models with incomplete data. (English) Zbl 1178.62040

Summary: In modeling complex longitudinal data, semiparametric nonlinear mixed-effects (SNLME) models are very flexible and useful. Covariates are often introduced in the models to partially explain the inter-individual variations. In practice, data are often incomplete in the sense that there are often measurement errors and missing data in longitudinal studies. The likelihood method is a standard approach for inference for these models but it can be computationally very challenging, so computationally efficient approximate methods are quite valuable. However, the performance of these approximate methods is often based on limited simulation studies, and theoretical results are unavailable for many approximate methods.
We consider a computationally efficient approximate method for a class of SNLME models with incomplete data and investigate its theoretical properties. We show that the estimates based on the approximate method are consistent and asymptotically normally distributed.

MSC:

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
65C60 Computational problems in statistics (MSC2010)
62H12 Estimation in multivariate analysis
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