Parameter estimation under constraints for multivariate normal distributions with incomplete data

This work presents an application of the EM-algorithm to two problems of estimation and testing in a multivariate normal distribution with missing data. The assumptions are that the observations are multivariate normally distributed and that the missing values are missing at random. The two models are tested applying the log-likelihood ratio test; for deriving the maximum likelihood estimates and evaluating the corresponding log-likelihood functions the EM algorithm is used. The problem of different and non-monotone patterns of missing data is solved introducing suitable transformations and partitions of the data matrix. The algorithm is proposed for general constraints on the mean vector; the topic of exchangeability of random vectors is also presented.