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Statistics Estimator Consistency

  1. Feb 13, 2010 #1
    1) Distribution is a uniform distribution on the interval (Ө, Ө+1)
    Show that Ө1 is a consistent estimator of Ө. Ө1=Ῡ -.5
    Show that Ө2 is a consistent estimator of Ө. Ө2=Yn – (n/(n+1)).

    2) I think the distribution for this one is a uniform distribution on the interval (0, Ө) but I am not 100% sure.
    Let Y1, Y2, …, Yn denote a random sample of size n from a power family distribution. Then the method in Section 6.7 imply that Yn=max(Y1, Y2, …, Yn ) has the distribution function of:
    0, y<0
    Fn(y)= (y/ Ө)^(αn) , 0 ≤ y ≤ Ө
    1, y> Ө

    Show that Yn is a consistent estimator of Ө.
     
    Last edited: Feb 13, 2010
  2. jcsd
  3. Feb 13, 2010 #2

    statdad

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    Homework Helper

    For 1 and 2 you need to state the distribution being sampled.
     
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