标题： 基于扰动平滑的线性混合效应状态空间模型估计 显示英文标题

标题： Estimating Linear Mixed-effects State Space Model Based on Disturbance Smoothing

摘要： 本文将线性混合效应状态模型扩展以适应相关个体，并研究基于扰动平滑的参数和状态估计。 对于参数估计，考虑了EM算法和基于评分的算法。首先研究了EM算法的中间量，从中推导出了两种给定模型的中间量最大化器的显式递归公式。 至于基于评分的算法，得到了评分向量的显式公式，从中可以看出最大似然估计等价于矩估计。 对于状态估计，我们主张在纵向观测稀疏时不应假设随机效应事先已知。为此，提出了一种名为带有核平滑的混合卡尔曼滤波器（MKF-KS）的算法。 进行了数值研究以调查所提出的算法，验证了所提出的推理方法的有效性。 显示英文摘要

摘要： We extend the linear mixed-effects state model to accommodate the correlated individuals and investigate its parameter and state estimation based on disturbance smoothing in this paper. For parameter estimation, EM and score based algorithms are considered. Intermediate quantity of EM algorithm is investigated firstly from which the explicit recursive formulas for the maximizer of the intermediate quantity are derived out for two given models. As for score based algorithms, explicit formulas for the score vector are achieved from which it is shown that the maximum likelihood estimation is equivalent to moment estimation. For state estimation we advocate it should be carried out without assuming the random effects being known in advance especially when the longitudinal observations are sparse. To this end an algorithm named mixture Kalman filter with kernel smoothing (MKF-KS) is proposed. Numerical studies are carried out to investigate the proposed algorithms which validate the efficacy of the proposed inference approaches.