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Math Help - pmf, MVUE

  1. #1
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    pmf, MVUE

    Let f=f(y;x),y>0 be a probability mass function that depends on the unknown parameter x, has continuous first and second order derivatives, and the support of f does not depend on the x.
    1.show that the constant estimator x'=x, where x is the true value, is a minumum variance unbiased estimator for x.
    2.what is the variance of x'?
    3.and why the Cramer-Rao lower bound for f is not necessarily lower bound for x'=x?
    Last edited by mr fantastic; March 13th 2010 at 04:57 PM. Reason: Restored deleted question. Thread closed as per SOP.
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  2. #2
    MHF Contributor matheagle's Avatar
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    you cannot estimate a parameter with itself.
    The variance of that constant would be zero by the way.
    and the expected value of a constant is that constant, so theta is unbiased for theta
    but theta is not a statistic, it depends on the unknown paramter
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  3. #3
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    but how can you explain that this estimator is the minimum variance unbiased estimator,this is true though ?
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