Fisher Information of a Function

Question

Fisher Information is defined as $I_{\lambda}=E[(\frac{\partial f(y,x)}{\partial \lambda})^2]$.

I want to show that $I_{g(\lambda)} = I_{\lambda}(g'(\lambda))^2$.

All I managed to do is

$I_{g(\lambda)} = E[(\frac{\partial f(y,x)}{\partial g(\lambda)})^2]= E[(\frac{\partial f(y,x)}{\partial \lambda} \frac{1}{g'(\lambda)})^2]$

This might be a simple mistake, but is this wrong? It seems not to give the desired result...

Answer 1

The correct property is : $$(g'(λ))^{2}I_{g(λ)}=I_λ$$

So your steps are correct, but your initial goal was wrong.