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Statistics- unbiased estimator #3

  1. Mar 1, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose that n=5 observations are taken from the uniform pdf, fY=1/[tex]\Theta[/tex] 0<y<[tex]\Theta[/tex]
    where [tex]\Theta[/tex] is unknown. Two unbiased estimators for [tex]\Theta[/tex] are

    [tex]\Theta[/tex]1= (6/5)*Ymax
    [tex]\Theta[/tex]2= (6)*Ymin

    which estimator would be better to use? hint: What must be true of Var(Ymax) and Var(Ymin) given that fy is symmetric ? Does your answer as to which estimator is better make sense on intuitive grounds ? Explain.


    2. Relevant equations

    Var(Y)=E[Y2] - E[Y]2

    Ymin=n*(1-FY(y))n-1fY(y)

    Ymax=n*(FY(y))n-1fY(y)

    3. The attempt at a solution

    I'm trying to calculate the variances of both the estimators and see which one is smaller.
    But, there is the extra information like, n=5 and that the distribution is symmetric, and I'm sure I need to use it.
    Plus, I don't know how to answer it on intuitive grounds.
    Would appreciate any help.
    Thanks.

    EDIT:

    Now, I am still trying to solve it, and if I know that the distribution is symmetric, the variance of Ymin and Ymax are the same.
    However, since the first estimator is divided by 5, we know that it's 1/25 of the variance of the second estimator.
    Can I say this ? Is this the"on intuitive grounds" answer that they are asking ?
    What about the sample size n=5 ? what do I do with it ?

    Thanks
     
    Last edited: Mar 1, 2010
  2. jcsd
  3. Mar 1, 2010 #2
    anybody ?

    can't figure it out :\
     
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