Motivated by better modeling of intra-individual variability in longitudinal data, we propose a class of location-scale mixed effects models, in which the data of each individual is modeled by a parameter-varying generalized hyperbolic distribution. We first study the local maximum-likelihood asymptotics and reveal the instability in the numerical optimization of the log-likelihood. Then, we construct an asymptotically efficient estimator based on the Newton-Raphson method based on the original log-likelihood function with the initial estimator being naive least-squares-type. Numerical experiments are conducted to show that the proposed one-step estimator is not only theoretically efficient but also numerically much more stable and much less time-consuming compared with the maximum-likelihood estimator.

翻译：受纵向数据中个体内变异性建模优化的启发，本文提出一类位置-尺度混合效应模型，该模型中每个个体的数据由参数变化的广义双曲分布进行建模。我们首先研究局部极大似然渐近性质，揭示了对数似然函数数值优化中的不稳定性。随后基于原始对数似然函数，采用以朴素最小二乘型估计为初始估计的牛顿-拉夫森方法，构建渐近有效估计量。数值实验表明，与极大似然估计量相比，所提出的单步估计量不仅具有理论有效性，而且在数值稳定性与计算耗时方面均具有显著优势。