Likelihood function
Definition taught in Estimation, part of Statistical inference
Likelihood function
| Type | Definition |
| Taught in | Estimation |
| Part | Statistical inference |
| Properties | 1 |
Let X_1,\ldots,X_n have joint mass or density function f(x_1,\ldots,x_n;\theta), and let x_1,\ldots,x_n be the observed values. The likelihood function is
L(\theta)=L(\theta;x_1,\ldots,x_n)=f(x_1,\ldots,x_n;\theta),\qquad \theta\in\Theta.
Properties
Invariance of maximum likelihood
Main article: Invariance of maximum likelihood
If \widehat\theta is the maximum likelihood estimator of \theta and g is a function, then the maximum likelihood estimator of g(\theta) is g(\widehat\theta).
Used in
- Taught in Estimation, where the derivation and examples are.
- All 5 questions on Estimation
See also
Continuous distribution · Estimator · Method of moments · Sample correlation coefficient · Maximum likelihood · Invariance of maximum likelihood · Unbiased estimator · Mean squared error