Question 3

Question 3. Suppose two independent multivariate random samples are collected, and they are denoted by 11 12 1n1 x and x, ,..., x 21 22 2n2 x , where n x, ,..., x 1 and n2 are the sample sizes and each xij is a p?1 vector. The first sample is collected from a population with mean ?1 and covariance matrix ?1 whilst the second sample from a population with mean ?2 and covariance matrix ?2. We assume these two samples are large, that is both n1 and n2 are large, however the populations distributions for these two samples are unknown. (a) Clearly explain how to test the hypothesis of H0: C ?1 = C ?2, where the C matrix is known and is r?p. You MUST provide the reasons for your test procedure. (b) Explain how to construct 100(1-?)% Bonferroni simultaneous confidence intervals for C (?1 - ?2).