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Math Help - uniform .does complete statistic exist?

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    uniform .does complete statistic exist?

    for X~Uniform[a-1/2,a+1/2]

    (X(1),X(n)) is minimal sufficient but it is not complete.

    Does a complete statistic exist in this case?

    There is a theorem that says that every complete sufficient statistic must be minimal sufficient.
    Is it true to conclude that if there is a minimal sufficient statistic and it is not complete, then there is no complete statistic (since the complete statistic would be a minimal sufficient statistic and therefore a 1-1 function of that minimal sufficient statistic)?

    Thanks


    OK, I figured it out.

    Found the following theorem

    Theorem. If T is complete and sufficient for the family, and a minimal
    sufficient statistic exists, then T is also minimal sufficient. (Lehmann &
    Scheff´e 1950)
    • If a minimal sufficient statistic is complete, then any minimal sufficient
    statistic is complete.
    If a minimal sufficient statistic is not complete, then there are no
    complete and sufficient statistics for the family.
    Last edited by lyann; May 30th 2010 at 11:12 AM. Reason: solved
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