Unbised estimator of Binomial Distribution

  • Thread starter leon1127
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  • #1
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[SOLVED] unbised estimator of Binomial Distribution

I have no idea how to find such an estimator
Suppose[tex]X_1, ..., X_n \sim Bern(p)
[/tex]
find an unbiased estimator of [tex]p^m, for m < n[/tex]
Induction on m was a nasty mess that should not be expected. The power of m causes some problem when I try to go from the definition of expectation. Any one have some hint?
 

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  • #2
EnumaElish
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Statistic u is unbiased if E = p^m. Suppose m = 2. To find u, you count all sequences that have two successes in a row, then express them as a ratio of the total number of trials. Would that satisfy E = p^2?
 
  • #3
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I approached in a similar way.
It is clear that [tex] Y = X_1....X_m [/tex] is unbiased for p^m. I was asked to find an unbiased estimator that is a function of sample total. Thus I construct a R.V which
[tex] Z(T) = 1 for T = 26; 0 elsewhere[/tex]
I might have to normalise Z so that it is the same as Y. However I dont know how to sum it.
 
  • #4
EnumaElish
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Where did 26 come from?

If you look at my previous post you will see that it is a function of the sample total.
 
  • #5
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it is not 26, it should be m.....
 
  • #6
EnumaElish
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Very well, my previous post applies.
 
  • #7
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k gotcha thx
 

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