On the use of the selection matrix in the maximum likelihood estimation of normal distribution models with missing data
On the use of the selection matrix in the maximum likelihood estimation of normal distribution models with missing data
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DOI：
10.1080/03610926.2017.1353631
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发表时间：
2018-07
期刊：
影响因子：
--
通讯作者：
Keiji Takai
中科院分区：
文献类型：
--
作者：
Keiji Takai
摘要在本文中，通过使用恒定和随机选择矩阵，得出了最大可能性（ML）估计值的几种属性和正态分布的ML估计值，而数据却丢失了。常数选择矩阵使我们能够获得ML估计的明确形式，以及EM算法与得分函数之间的确切关系。随机选择矩阵使我们能够阐明ML估计器一致性的证据，从而通过EM算法得出序列的渐近性能，并推导信息矩阵。
ABSTRACT In this article, by using the constant and random selection matrices, several properties of the maximum likelihood (ML) estimates and the ML estimator of a normal distribution with missing data are derived. The constant selection matrix allows us to obtain an explicit form of the ML estimates and the exact relationship between the EM algorithm and the score function. The random selection matrix allows us to clarify how the missing-data mechanism works in the proof of the consistency of the ML estimator, to derive the asymptotic properties of the sequence by the EM algorithm, and to derive the information matrix.