The Gaussian mixed-effects model driven by a stationary integrated Ornstein-Uhlenbeck process has been used for analyzing longitudinal data having an explicit and simple serial-correlation structure in each individual. However, the theoretical aspect of its asymptotic inference is yet to be elucidated. We prove the local asymptotics for the associated log-likelihood function, which in particular guarantees the asymptotic optimality of the suitably chosen maximum-likelihood estimator. We illustrate the obtained asymptotic normality result through some simulations for both balanced and unbalanced datasets.

翻译：由平稳积分奥恩斯坦-乌伦贝克过程驱动的高斯混合效应模型已被用于分析具有显式且简单个体内序列相关结构的纵向数据。然而，其渐近推断的理论方面仍有待阐明。我们证明了相关对数似然函数的局部渐近性，这尤其保证了适当选择的最大似然估计量的渐近最优性。我们通过平衡与非平衡数据集的仿真实验，展示了所获得的渐近正态性结果。