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Bernoulli estimator

  1. Jun 1, 2012 #1
    A Bernoulli random sample :

    X=1 , Pr(X=1)=p;
    X=0 , Pr(X=0)=1-p;

    taken X1, ..., Xn

    and if it is known that 0=< p =<0.5

    find a method of moments estimator of p

    If I just take estimator of P =(sum Xi )/n than the estimate p may be bigger than 0.5 as in extreme case all Xi =1 .
    What should I do , take estimator of p = Max (0.5*n , Sum Xi) /n ?
     
  2. jcsd
  3. Jun 1, 2012 #2
    Just simply state that fact, that is

    P= sum Xi /n if sum Xi /n < 0.5
    P= 0.5 otherwise.
     
  4. Jun 1, 2012 #3
    But... is it too artificial?
    Pr( estimator (p) = 0.5 ) is slightly bigger ...?
     
  5. Jun 1, 2012 #4
    Artificial? You like better min( sum Xi/n, 0.5) ?

    No, p will not be generally bigger and you will rarely get estimations of 0.7 or 0.8, remember that they already assure you that the real p is no higher than 0.5

    Adjusting the estimation makes the value p=0.5 more common but that is irrelevant and only makes the estimation more accurate.
     
    Last edited: Jun 1, 2012
  6. Jun 1, 2012 #5
    Thank you so much !
     
  7. Jun 2, 2012 #6
    You're welcome :smile:
     
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