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Statistics: Difference between revisions
→Fisher Information
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* <math>I(\theta) = E[ (\frac{\partial}{\partial \theta} \log f(X; \theta) )^2 | \theta]</math> | * <math>I(\theta) = E[ (\frac{\partial}{\partial \theta} \log f(X; \theta) )^2 | \theta]</math> | ||
* or if <math>\log f(x)</math> is twice differentiable <math>I(\theta) = -E[ \frac{\partial^2}{\partial \theta^2} \log f(X; \theta) | \theta]</math> | * or if <math>\log f(x)</math> is twice differentiable <math>I(\theta) = -E[ \frac{\partial^2}{\partial \theta^2} \log f(X; \theta) | \theta]</math> | ||
* <math>I_n(\theta)</math> is the fisher information of the sample. Replace <math>f</math> with your full likelihood. | * <math>I_n(\theta) = n*I(\theta)</math> is the fisher information of the sample. Replace <math>f</math> with your full likelihood. | ||
====Cramer-Rao Lower Bound==== | ====Cramer-Rao Lower Bound==== | ||