Multivariate sampling

Abstract

The basic tools for manipulating random samples from a multivariate distribution are developed in this chapter. We introduce random matrices in Section 6.2 and show the usefulness of the “vec operator” and Kronecker product in this regard. Also, the matrix variate normal distribution is defined and its basic properties are explained. Section 6.3 deals with theorems in the “asymptotic world” as the sample size goes to infinity. These are the central limit theorem, a general Slutsky theorem, and the so-called delta method.