Suppose that we have random vector samples from a multivariate normal distribution, say

Np(,). In Chapter 7, we saw testing problems for the univariate normal distribution. If the

variance-covariance matrix is known to be a diagonal matrix, that is components are uncorrelated

random variables, we can revert back to the methods discussed there. However, this

is not generally the case for multivariate distributions and they need specialized methods for

testing hypothesis problems.

For the problem of testing H = 0 against K 0, we consider two cases here:

(i) is known, and (ii) is unknown. Suppose that we have n samples of random vectors

from Np(, ), which we will denote as {X1,X2, ,Xn}. The sample of random vectors is

the same as saying that we have iid random vectors. 1.and give interpretations of your results. What is a reasonable interpretation of this statistical test? Construct confidence regions for each problem to aide your interpretations. How might this process compare to testing each univariate variable independently and what problems might that incur?