A Note on the Sphericity Test
A Note on the Sphericity Test
Let $x$ be a random $p \times 1$ column vector having a multivariate normal distribution with unknown mean vector $\mu$ and unknown covariance matrix $\Sigma$. We wish to test the hypothesis of "sphericity," namely $H:\Sigma = \sigma^2I_p$, where $\sigma^2 > 0$ is an unknown positive constant. Alternatives to $H$ which …