APPLIED MULTIVARIATE STATISTICS: WITH SAS® SOFTWARE

1.4. Sampling from Multivariate Normal Populations

Suppose we have a random sample of size n, say y1, ..., yn, from the p dimensional multivariate normal population N_p(μ, Σ). Since y1, ..., yn are independently and identically distributed (iid), their sample mean

is also normally distributed as N_p(μ, Σ/n). Thus, is an unbiased estimator of μ. Also, observe that has a dispersion matrix which is a multiple of the original population variance-covariance ...