Chp13 Q13.12

[Amit_Bansal]

here to find MLE of sigma^2 , we differentiate w.r.t sigma. Why didn't we differentiate w.r.t sigma^2 ??

 

[bapan]

Yes, you can.
Try it. You should get the same answer in the end.

 

[John Lee]

here to find MLE of sigma^2 , we differentiate w.r.t sigma. Why didn't we differentiate w.r.t sigma^2 ??

It's to do with the invariance property of MLEs. So if we find the estimate for σ then the estimate for σ² is just the square of the first estimate.