Invariance of the maximum likelihood estimator
Proposition taught in Estimation and inference for the multivariate normal, part of Statistical learning
Invariance of the maximum likelihood estimator
| Type | Proposition |
| Taught in | Estimation and inference for the multivariate normal |
| Part | Statistical learning |
Let the distribution of the data depend on \theta=(\theta_1,\ldots,\theta_k), with maximum likelihood estimator \widehat\theta. Let \tau(\theta)=(\tau_1(\theta),\ldots,\tau_r(\theta)), 1\le r\le k, be a transformation of the parameter. Then the maximum likelihood estimator of \tau_l(\theta) is \widehat\tau_l=\tau_l(\widehat\theta).
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 maximum likelihood · Maximum likelihood · Likelihood function · Estimator · Wishart distribution · Sampling law of the normal mean and scatter · Multivariate central limit theorem · The limit of Hotelling’s statistic