Studentised coefficient pivot
Corollary taught in Bayesian linear regression, part of Bayesian statistics
Studentised coefficient pivot
| Type | Corollary |
| Taught in | Bayesian linear regression |
| Part | Bayesian statistics |
\frac{\widehat\beta_j-\beta_j}{s\sqrt{c_{jj}}} \sim t_{n-p}. Thus \widehat{\boldsymbol{\beta}} itself has the normal distribution Equation (10) in Bayesian linear regression; the Student distribution appears only after replacing the unknown \sigma by s and standardising.
Used in
- Taught in Bayesian linear regression, where the derivation and examples are.
- All 8 questions on Bayesian linear regression
See also
Normal distribution · Gaussian linear model · Error and residual · Ordinary least squares · Sampling distribution of the OLS estimator · Least-squares decomposition · Conditional coefficient posterior · Marginal variance posterior