I get h(x1,...,xn)=1 and I'm wondering if this is correct.
Jan 9th 2010, 08:32 PM
I had to reread this many times
YOU need to state the density
Seeing an alpha and a beta I'm guessing your underlying density is a gamma
so show me your work, especially the density
Jan 10th 2010, 07:13 AM
Can't believe I forgot the density; it's as you said a gamma.
I'm wondering would my be the same as the product of PDFs as I mentioned above in this post?
Jan 10th 2010, 07:19 AM
you're missing a negative sign in the exponent of the exponential
and IT's a 6 not a theta in that exponent, which solves your problem
The product of the x's and the theta cannot be separated, giving you the product as the suff stat.
Jan 10th 2010, 07:32 AM
So would cause that's where I'm having a problem with.
Jan 10th 2010, 07:40 AM
The function of the data (xi's) that canot be separated from theta is
Hence is suff for theta
Jan 10th 2010, 08:06 AM
And since doesn't depend on theta, Y is a sufficient estimator of theta.
EDIT: Didn't see your previous post.
Saved my neck once again. Sorry for being such an idiot.
Jan 10th 2010, 08:40 AM
NO, its that part that is stuck with theta that is suff.
The product is suff for theta because of the theta in the expoenent of the product
that one over the product part that can go into h function (it's garbage)
The key term is
The is garbage that can go into h
Jan 10th 2010, 08:54 AM
Really? Cause that's what my book implies in a similar example:
Since does not depend on theta, is a sufficient statistic for theta.