ABSTRACT

In this chapter, we review several basic features of the multivariate normal distribution. Section 3.2 considers general properties of the multivariate normal density and Section 3.3 considers the sampling distribution of the maximum likelihood estimators (MLEs) of the mean vector and variance–covariance matrix based on iid (independent, identically distributed) random sampling of a multivariate normal distribution. Section 3.4 reviews the standard conjugate distributions for Bayesian inference with the multivariate normal distribution and Section 3.5 considers various generalizations and robustifications of the normal model. The properties of the multivariate normal distribution are well known and available in many places; our primary sources are the texts by Johnson and Wichern (1998) and Morrison (2005). A classic and comprehensive treatment is given by Anderson’s (2003) text.