hello there,
I need some help with this question.
X1,...Xn~f(x,theta)
f(x,theta)=exp{-(x-theta)}exp{-exp{-(x-theta)}}
( look picture attached )
find the Cramer Rao lower bound for the unbiased estimator of theta.
cheers !
Hello,
Assuming the Xi are independent... This is how I've been taught. Dunno how you've learnt it...
We have the joint pdf of the Xi equal to :
An estimator will be solution of
Thus
Wow...now, that's ugly !
I've been taught to find Fisher's information, and h such that
(if it's an unbiased estimator, then h=Id)
And then Cramer Rao's lower bound is