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Math Help - UMVUE of geometric sample

  1. #1
    Junior Member
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    Feb 2010
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    43

    UMVUE of geometric sample

    Hi,

    I have a an iid sample from a geometric (p) distribution. I found that the complete sufficient statistic is  \sum_{i=1}^n x_i using "full exponential family with open set."

    I am trying to find the UMVUE of  \tau (p) = E_p {X_1} .

    I am arguing that the expectation of  X_1 equals the expectation of my complete sufficient statistic and thus I use it as my estimator and it is unbiased. Furthermore, because the unbiased estimator is also complete, I am guaranteed that it is UMVUE.

    Is that a tight argument or do I actually need to go through the steps of finding the conditional expectation? (I did find the related post of http://www.mathhelpforum.com/math-help/advanced-probability-statistics/86748-need-help-statistics-problem.html)

    I'd appreciate any feedback! Thank you!
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  2. #2
    Junior Member
    Joined
    Feb 2010
    Posts
    43

    parameters to be estimated

    Hi,

    Am I on the right track by noting that the parameter that I am trying to estimate is 1/p, while the discussion in the link is trying to estimate p?

    Thank you!
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