Category:Fréchet-Darmois-Cramér-Rao Inequality

This category contains pages concerning Fréchet-Darmois-Cramér-Rao Inequality:

Let $S$ be a sample of $n$ observations from a probability distribution with frequency function $\map f {x, \theta}$.

Let it be assumed that certain regularity conditions apply.

Let it also be assumed that the extremes do not depend on $\theta$.

This article, or a section of it, needs explaining. In particular: what those conditions are You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code.

The lower bound of the variance of an estimator $T$ of a parameter $\theta$ is given by $\dfrac 1 I$ where:

$I = -n \map E {\dfrac {\partial^2 \ln f} {\partial \theta^2} }$

Source of Name

This entry was named for Maurice René Fréchet, Georges Darmois, Carl Harald Cramér and Calyampudi Radhakrishna Rao.