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 !

(Hi)

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- May 25th 2009, 06:47 AMWeeGCramer Rao
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 !

(Hi) - May 25th 2009, 12:30 PMMoo
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 ! :eek:

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 - May 29th 2009, 01:44 PMWeeG
it is ugly !

(Doh)

anyone knows how to finish it ?