MathLiveCramér–Rao bound
It gives a lower limit on the variance of any unbiased estimator T of a parameter function \psi(\theta), based on the Fisher information. It is used to judge how efficient an estimator can possibly be.
\operatorname{var}(T) \geq \frac{[\psi'(\theta)]^2}{I(\theta)}What the symbols mean
| variance of the estimator T | |
| the parameter function being estimated, with derivative \psi'(\theta) | |
| derivative of \psi with respect to the parameter \theta | |
| Fisher information about \theta contained in the sample |
About this formula
- FieldStatistics
- TopicStatistical estimation
- LevelUniversity
- Also calledCramér-Rao lower bound, Cramer-Rao lower bound, Cramér-Rao inequality, Cramer-Rao inequality, CRLB, variance lower bound for estimators
- SourceWikidata Q1138810
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