Sampling law of the normal mean and scatter
Theorem taught in Estimation and inference for the multivariate normal, part of Statistical learning
Sampling law of the normal mean and scatter
| Type | Theorem |
| Taught in | Estimation and inference for the multivariate normal |
| Part | Statistical learning |
Under independent sampling from \operatorname{N}_p(\boldsymbol{\mu},\Sigma), the sample mean and the corrected cross-product matrix are independent, with
\overline{\mathbf{X}}\sim\operatorname{N}_p\bigl(\boldsymbol{\mu},\,\tfrac1n\Sigma\bigr), \qquad A\sim W_p(\Sigma,\,n-1), \qquad \overline{\mathbf{X}}\ \text{independent of}\ A.
Used in
- Taught in Estimation and inference for the multivariate normal, where the derivation and examples are.
- All 9 questions on Estimation and inference for the multivariate normal
See also
Invariance of the maximum likelihood estimator · Wishart distribution · Multivariate central limit theorem · The limit of Hotelling’s statistic · Null distribution of Hotelling’s · Two-sample Hotelling test · Likelihood of a multivariate normal sample · Maximum likelihood for a normal mean vector