Part III: Inference using the Multivariate Normal Distribution (MVN)

Part III of this module covers statistical inference based on the multivariate normal (MVN) distribution.

Chapter 7 focuses on classical distribution theory relating to the MVN distribution, including the Wishart distribution, which is defined on the set of symmetric positive definite matrices and is a natural generalisation of the \(\chi^2\) distribution. Another important distribution related to the MVN distribution is the Hotelling \(T^2\) distribution, which is a multivariate analogue of the Student’s \(t\)-distribution. The Wishart and Hotelling \(T^2\) distributions then allow us to conduct hypothesis tests concerning vector means in \(1\)-sample and \(2\)-sample settings.

Chapter 10 is concerned with the multivariate linear model, in which the responses consist of random vectors rather than single random variables. Errors in this setting take the form of random vectors.