Show pageOld revisionsBacklinksExport to PDFBack to top This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== Fisher information ====== The Fisher information roughly describes how much information a random variable gives about an unknown parameter of its distribution. It is defined as: $$I(\theta) = {\rm Var}[\ell'(\theta)] = -\mathbb{E}[\ell''(\theta)]$$ From the Fisher information, we can derive the asymptotic variance of the parameter. $$\sqrt{n}(\hat{\theta}_n^{MLE} - \theta^*) \xrightarrow[n \to \infty]{(d)} \mathcal{N}(0, \frac{1}{I(\theta^*)})$$ where $\theta^*$ is the true parameter, and $\hat{\theta}_n^{MLE}$ is the MLE of the parameter. kb/fisher_information.txt Last modified: 2024-04-30 04:03by 127.0.0.1