Maximum likelihood estimators in growth curve model with monotone missing data
Maximum likelihood estimators in growth curve model with monotone missing data
复制标题
单调缺失数据增长曲线模型中的最大似然估计
DOI：
10.1080/01966324.2020.1791290
复制
发表时间：
2021
影响因子：
--
通讯作者：
Y.
中科院分区：
文献类型：
--
作者：
Yagi;A.;Seo;T. and Fujikoshi;Y.
本文重点介绍当数据集具有单调缺失模式时，增长曲线模型的单样本版本中的平均参数向量和协方差矩阵的最大似然估计量 (MLE)。首先，当协方差矩阵已知时，获得平均参数向量的 MLE 的闭合形式。类似地，当平均参数向量已知时，可以得到协方差矩阵的 MLE。还给出了这些估计量的分布及其基本属性。然后，考虑到这些表达式给出了似然性或确定方程，我们提出了一种算法，其中包括迭代过程，以便在所有参数未知时获得 MLE。此外，还提出了平均参数向量的传统估计器。最后，给出一个数值例子来说明我们的估计过程。
This article focuses on the maximum likelihood estimators (MLEs) of the mean parameter vector and the covariance matrix in a one-sample version of the growth curve model when the dataset has a monotone missing pattern. First, a closed form is obtained for the MLE of the mean parameter vector when the covariance matrix is known. Similarly, it is obtained for the MLE of the covariance matrix when the mean parameter vector is known. The distributions of these estimators and their basic properties are also given. Then, considering that these expressions give the likelihood or determining equations, we propose an algorithm that includes an iterative procedure to obtain the MLEs when all the parameters are unknown. Further, a conventional estimator for the mean parameter vector is also proposed. Finally, a numerical example is given to illustrate our estimation procedure.