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Math Help - Finding minimum variance unbiased estimator (MVUE)

  1. #1
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    Finding minimum variance unbiased estimator (MVUE)

    Random sample Y1,....,Yn with pdf:
    f(y|θ) = 3y^2/θ^3, 0<y<θ and 0 elsewhere

    Given Y(n) = max(Y1,...,Yn) is sufficient for θ,
    a) Show that Y(n) has pdf:
    f(n)(y|θ) = 3ny^(3n-1)/θ^(3n) , 0<y<θ and 0 elsewhere

    b) Find MVUE for θ


    I am unsure as to how to start these so any help is appreciated
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  2. #2
    MHF Contributor matheagle's Avatar
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    The largest order statistic, i.e., the max is sufficient for theta.
    Next, as you are asked to do, obtain the density of this order stat.

    Use nf(x)[F(x)}^(n-1)
    Then otain the expected value of the max and compare that to theta.
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