Maximum Likelihood Estimation of μ and Σ from a Multivariate Normal Distribution

Abstract

In finding the maximum likelihood estimators of the parameters of a multivariate normal distribution, the following derivation first diagonalizes the covariance matrix and then maximizes the likelihood by the choice of the elements of the transformed mean and the latent roots of the covariance matrix. Multivariate calculus is used to verify quickly and simply that the likelihood is indeed maximized.

Key Words:

• Latent roots