Asymptotic properties for a simulated pseudo maximum likelihood estimator

We propose an estimator for parameters of nonlinear mixed effects model, obtained by maximization of a simulated pseudo likelihood. This simulated criterion is constructed from the likelihood of a Gaussian model whose means and variances are given by Monte Carlo approximations of means and variances of the true model. If the number of experimental units and the sample size of Monte Carlo simulations are respectively denoted by N and K, we obtained the strong consistency and asymptotic normality of the estimator when the ratio NJ/2 /K tends to zero