# how to find the UMVUE of the location parameter under t distribution

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• April 2nd 2010, 06:28 PM
egpivo
how to find the UMVUE of the location parameter under t distribution
$

f(x;\theta)={{\Gamma({{v+1}\over2})}\over{\Gamma({ v\over2})\sqrt{\pi v}}}\Big(1+\frac{(x-\theta)^2}{v}\Big)^{-\frac{v+1}{2}}
, v > 3
$

i have no idea how to create the UMVUE of $\theta$, and please help me , give me some tips.. thx
• April 2nd 2010, 10:22 PM
matheagle
I assume v is fixed.
So find a sufficient stat for theta and go from there.
Obtain the likelihood function and apply the factorization theorem to find your suff stat.
• April 2nd 2010, 10:37 PM
egpivo
Quote:

Originally Posted by matheagle
I assume v is fixed.
So find a sufficient stat for theta and go from there.
Obtain the likelihood function and apply the factorization theorem to find your suff stat.

But how about the completeness? thx!