Sampling distribution of the OLS estimator
Proposition taught in Bayesian linear regression, part of Bayesian statistics
Sampling distribution of the OLS estimator
| Type | Proposition |
| Taught in | Bayesian linear regression |
| Part | Bayesian statistics |
\widehat{\boldsymbol{\beta}}\mid{\boldsymbol{\beta}},\sigma^2,{\color{blue}\boldsymbol{X}} \sim\operatorname{N}_p\!\left( {\boldsymbol{\beta}},\sigma^2({\color{blue}\boldsymbol{X}}^\top{\color{blue}\boldsymbol{X}})^{-1}\right). Also, \frac{\operatorname{SSE}}{\sigma^2}\sim\chi^2_{n-p}, \qquad \widehat{\boldsymbol{\beta}}\ \text{is independent of }\operatorname{SSE}.
Used in
- Taught in Bayesian linear regression, where the derivation and examples are.
- All 8 questions on Bayesian linear regression
See also
Gaussian linear model · Error and residual · Ordinary least squares · Studentised coefficient pivot · Least-squares decomposition · Conditional coefficient posterior · Marginal variance posterior · Marginal Student posterior