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：---- 高斯混合效应模型驱动的平稳积分奥恩斯坦-乌伦贝克过程已被用于分析具有每个个体明确且简单的串行相关结构的纵向数据。然而，其渐近推断的理论方面尚未得到阐明。我们证明了相关对数似然函数的局部渐近性，这特别保证了适当选择的最大似然估计量的渐近最优性。我们通过一些平衡和非平衡数据集的模拟说明了获得的渐近正态性结果。