MathLiveFisher information
Gives the amount of information that an observed random variable carries about an unknown parameter of its distribution, computed as the expected square of the score function. It is used in statistical estimation, for example to find the Cramer-Rao lower bound on estimator variance.
I(\theta)=\mathbb{E}\left[\left.\left(\frac{\partial}{\partial\theta}\log f(X;\theta)\right)^2\right|\theta\right]What the symbols mean
| Fisher information about the parameter \theta | |
| unknown parameter of the distribution | |
| random variable with the modelled distribution | |
| probability density or mass function of X given parameter \theta | |
| expectation taken over X |
About this formula
- FieldStatistics
- TopicStatistical estimation
- LevelUniversity
- Also calledFisher information formula, expected squared score, amount of information about a parameter, score variance
- SourceWikidata Q1420659
Write it in Obsidian
MathLive is a free visual math editor for Obsidian. Run Find a formula, type “fisher information”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.