论文标题
基于广义双曲线分布的混合效应位置尺度模型
Mixed-effects location-scale model based on generalized hyperbolic distribution
论文作者
论文摘要
我们提出了一类位置尺度混合效应模型的更好建模，在纵向数据中的个体变异性上进行了更好的建模，其中每个人的数据由参数变化的广义双曲线分布建模。我们首先研究了局部最大似然的渐近性，并揭示了对数似然的数值优化时的不稳定性。然后，我们基于基于原始的对数可能函数的牛顿 - 拉夫森方法构建一个渐近有效的估计量，初始估计器是天真的最小二乘类型。进行了数值实验，以表明所提出的一步估计量不仅在理论上是有效的，而且在数值上也更加稳定，而且与最大样本估计量相比，既耗时又耗时少得多。
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.
