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Fisher's Estimator Inequality

Given $T$ an Unbiased Estimator of $\theta$ so that $\left\langle{T}\right\rangle{}=\theta$. Then

\begin{displaymath}
\mathop{\rm var}\nolimits (T) \geq {1\over N\int_{-\infty}^\infty \left[{\partial(\ln f)\over\partial\theta}\right]^2 f\,dx},
\end{displaymath}

where $\mathop{\rm var}\nolimits $ is the Variance.




© 1996-9 Eric W. Weisstein
1999-05-26