# Given an MLE $\hat{\theta}$, how to show $f(\hat{\theta})$ is also an MLE?

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.

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