On the Likelihood Ratio Test of a Normal Multivariate Testing Problem II
On the Likelihood Ratio Test of a Normal Multivariate Testing Problem II
Let the random vector $X = (X_1 \cdots X_p)'$ have a multivariate normal distribution with unknown mean $\xi$ and unknown nonsingular covariance matrix $\Sigma$. Write $\bar\Gamma = \Sigma^{-1}\xi = (\Gamma_1, \Gamma_2, \Gamma_3)'$, where $\Gamma_1, \Gamma_2$ and $\Gamma_3$ are subvectors of $\bar\Gamma$ containing first $q$, next $p' - q$ and last …