# Is there any relationship between efficiency and correlation coefficient?

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)

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

$$r=\dfrac{COV(t_1,t_2)}{\sqrt{V(t_1)V(t_2)}}$$

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

I am not sure how to proceed now .

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