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Math Help - how to find the UMVUE of the location parameter under t distribution

  1. #1
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    how to find the UMVUE of the location parameter under t distribution

    <br /> <br />
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}}<br />
,  v > 3<br />

    i have no idea how to create the UMVUE of \theta, and please help me , give me some tips.. thx
    Last edited by egpivo; April 2nd 2010 at 10:30 PM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    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.
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  3. #3
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    Quote Originally Posted by matheagle View Post
    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!
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