Given an injective function $f: \Theta \rightarrow \mathbb{R}$ and an MLE $\hat{\theta}$ of $\theta ^*$, how do I prove that $f(\hat{\theta})$ is an MLE of $f(\theta^*)$. I know that because $f$ is injective, we can say

$L(\theta ^*) = L(f^{-1}(f(\theta ^*)))$. But I do not know how to use this in the proof.

  • $\begingroup$ Search for 'invariance' property of MLE. $\endgroup$ – StubbornAtom Jan 17 at 13:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.