ABSTRACT
In linear models, statistical inferences such as parameter estimation and hypothesis testing are usually expressed in some linear or quadratic forms of normal variables. Under some mild conditions, the quadratic form of normal variables may follow a chi-square distribution. The chapter provides some fundamental concepts of a multivariate normal, a chi-square, and a multivariate t distribution and their statistical properties. It presents a definition of a multivariate normal based on its probability density function. The chapter examines some statistical properties of a multivariate normal vector. It discusses the quadratic form of normal variables and its related chi-square distribution. The chapter addresses the study of the independence between quadratic forms or linear and quadratic forms of normal variables. It focuses on the multivariate t distribution and its statistical properties. Multivariate normal vector of correlated components can be transformed to be a multivariate normal vector of independent components.
