Originally Posted by

**alyosha2** I'm having a really hard time understanding this.

The MLE of a function of a parameter is the function of the MLE of the parameter.

That is if $\displaystyle t = h(\theta)$ and $\displaystyle \hat{\theta}$ is the MLE of $\displaystyle \theta$, then the MLE of $\displaystyle t$ is $\displaystyle \hat{t} = h(\hat{\theta})$

Ok, so the MLE of a function of a parameter is the same function with the MLE of the parameter fed into it. That's my understanding.

But the next claim is that for any square of a parameter the MLE of the square of the parameter will be the square of the MLE of the parameter. I just can't see how this follows.