Unbiased estimator of product of variance and expected value

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I would like to know if it is possible to find an unbiased estimator for the product of the variance of a random variable and its expected value.



And in general, an unbiased estimator of the product of a central moment of a random variable and its expected value.



I'm aware of Polyaches (unbiased estimators of products of central moments) and PolyRaws (unbiased estimators of products of raw moments). But what about the product of central and raw moments?







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    up vote
    0
    down vote

    favorite












    I would like to know if it is possible to find an unbiased estimator for the product of the variance of a random variable and its expected value.



    And in general, an unbiased estimator of the product of a central moment of a random variable and its expected value.



    I'm aware of Polyaches (unbiased estimators of products of central moments) and PolyRaws (unbiased estimators of products of raw moments). But what about the product of central and raw moments?







    share|cite|improve this question






















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I would like to know if it is possible to find an unbiased estimator for the product of the variance of a random variable and its expected value.



      And in general, an unbiased estimator of the product of a central moment of a random variable and its expected value.



      I'm aware of Polyaches (unbiased estimators of products of central moments) and PolyRaws (unbiased estimators of products of raw moments). But what about the product of central and raw moments?







      share|cite|improve this question












      I would like to know if it is possible to find an unbiased estimator for the product of the variance of a random variable and its expected value.



      And in general, an unbiased estimator of the product of a central moment of a random variable and its expected value.



      I'm aware of Polyaches (unbiased estimators of products of central moments) and PolyRaws (unbiased estimators of products of raw moments). But what about the product of central and raw moments?









      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Aug 16 at 23:20









      Ivan

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