Maximum likelihood estimation for multivariate normal distribution with hierarchical missing data

Jianqi Yu, Xiang Wang
2021 International Journal of Statistics and Applied Mathematics  
Closed forms are obtained for the maximum likelihood estimators (MLE) of the mean vector and the covariance matrix of a multivariate normal model with a hierarchical missing pattern. According to the missing pattern, the likelihood function is decomposed as product of several independent normal and conditional normal likelihood functions. The original parameters are transformed into a new set of parameters whose MLE are easy to derive. Since the MLE are invariant, the MLE of the original parameters are derived using the inverse transformation.
doi:10.22271/maths.2021.v6.i3a.681 fatcat:djtwd3ckfzgzri5vkda3flgbdq