A unified approach to estimation of nonlinear mixed effects and Berkson measurement error models

Mixed effects models and Berkson measurement error models are widely used. They share fea- tures which the author uses to develop a unified estimation framework. He d eals with models in which the random effects (or measurement errors) have a general parametric distribution, whereas the random regres- sion coefficients (or unobserved predictor variables) and error term s have nonparametric distributions. He proposes a second-order least squares estimator and a simulation-based estimator based on the first two mo- ments of the conditional response variable given the observed covariates. He shows that both estimators are consistent and asymptotically normally distributed under fairly general co nditions. The author also reports Monte Carlo simulation studies showing that the proposed estimators perform satisfactorily for relatively small sample sizes. Compared to the likelihood approach, the proposed methods are computationally feasi- ble and do not rely on the normality assumption for random effects or other variables in the model. Une strat´ egie d'estimation commune pour les mod` eles non lin´ eaires `

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