International Journal of Statistics and Applied Mathematics
2021, Vol. 6, Issue 3, Part A
Maximum likelihood estimation for multivariate normal distribution with hierarchical missing data
Author(s): Jianqi Yu and Xiang Wang
Abstract: 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.