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Thread: Sufficent statistics and unbiased

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    Sufficent statistics and unbiased




    If I find the (unique) sufficient statistic of a parameter and say I also found the MLE of the parameter. If the MLE of the parameter is not equivalent to the sufficient statistic, is this equivalent to saying that the MLE is biased?

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    Re: Sufficent statistics and unbiased

    I hope I haven't forgotten all my math stats, here' goes:

    Poisson: sum is sufficient stat; mle is the average, which is unbiased
    so, to specifically answer your question (assuming I understand correctly): no
    The mathematical explanation of a statistical procedure is really just pseudo-code, which we can make operational by translating it into real computer code. --B. Klemens

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    Re: Sufficent statistics and unbiased


    An interesting little question!

    Quote Originally Posted by stephanie View Post
    If I find the (unique) sufficient statistic of a parameter and say I also found the MLE of the parameter. If the MLE of the parameter is not equivalent to the sufficient statistic, is this equivalent to saying that the MLE is biased?
    I don't think (believe) that you can make such a conclusion.

    Maybe it could help to read about in wikipedia about sufficiency and ancillary statistics.

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