Let $t_1$ be the most efficient estimator and $t_2$ be the less efficient estimator with efficiency $e$ and let $r$ be correlation coefficient between the two estimator $t_1$ and $t_2$.Define relationship between $e$ and $r$.

So ofcourse $V(t_1)<V(t_2)$

Now I am not sure if $e=\dfrac{V(t_1)}{V(t_2)}$ or $e=\dfrac{V(t_2)}{V(t_1)}$ because in question it does not say relative efficiency with respect to $t_1$ or $t_2$.

I tried with both of them taking $e=\dfrac{V(t_1)}{V(t_2)}$ for now


$ \ \ =\dfrac{E(t_1t_2)-E(t_1)Et_2)}{{{eV(t_2)}}}$

I am not sure how to proceed now .

  • $\begingroup$ There is a relation if you are looking at the class of unbiased estimators of some function of $\theta$, your parameter of interest. $\endgroup$ – StubbornAtom Jan 11 at 18:30

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.