Testing for autocorrelation and random-effects in nonlinear mixed effects models based on <i>M</i>-estimation

<i>M</i>-estimation (robust estimation) for the parameters in nonlinear mixed effects models using Fisher scoring method is investigated in the article, which shares some of the features of the existing maximum likelihood estimation: consistency and asymptotic normality. Score tests for autocorrelation and random effects based on <i>M</i>-estimation, together with their asymptotic distribution are also studied. The performance of the test statistics are evaluated via simulations and a real data analysis of plasma concentrations data.