Sampling from the Multivariate Normal Distribution
Налини Равишанкер, Zhiyi Chi, Dipak K. Dey · 2021
We construct the joint density of a random sample from a multivariate normal distribution and describe estimation of the parameters of the distribution along with properties of these estimates. While most of these results, such as results related to the Wishart distribution, are only related to the multivariate linear model that we discuss in Section 13.1 , we include them here for the sake of completeness and since knowledge of these ideas are becoming increasingly more important in multivariate and high-dimensional linear models. Based on random samples, we describe inference for simple, multiple, and partial correlation coefficients, as well as some notions related to assessing multivariate normality. Readers may defer Chapter 6 for later, and go directly to Chapter 7 to continue with inference for the general linear model that we discussed in Chapter 4 .