Testing for Autocorrelation and Random-effects in Nonlinear Mixed Effects Models Based on M-estimation^*

M-estimation (robust estimation) for the parameters in nonlinear mixed effects models using Fisher scoring method is investigated in the paper, 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 M-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.

本文研究了采用费希尔得分法（Fisher scoring method）的非线性混合效应模型（nonlinear mixed effects models）的参数M估计（M-estimation，稳健估计）问题。该方法具备现有极大似然估计（maximum likelihood estimation）的部分特性：一致性与渐近正态性。本文还针对基于M估计的自相关（autocorrelation）与随机效应（random effects）得分检验（score tests）及其渐近分布展开了研究。此外，本文通过模拟实验与血浆浓度数据集的实际数据分析，对该检验统计量（test statistics）的性能进行了评估。