Maximum Likelihood Estimation of the Parameters of a Multivariate Normal Distribution
STANFORD UNIV CA DEPT OF STATISTICS
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This paper provides an exposition of several altnerative techniques used to obtain maximum likelihood estimators for the parameters of a multivariate normal distribution. In particular, matrix differentiation, matrix transformations and induction are treated. These techniques are used to derive the maximum likelihood estimators of the covariances of a Wishart distribution, of the covariances when there are missing observations, and of the means under a rank constraint. Although the paper is mainly expository, some of the proofs are new.
- Statistics and Probability