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.
MATHEMATICS SUBJECT CLASSIFICATION:
Funding
This work was supported by JSPS KAKENHI Grant Number 26730022.