# Estimator: Rao-BlackwellWatch

#1
iid discrete random variables with

for r=1,2,....

Determine a one-dimensional sufficient statistic for p and then by first finding a simple unbiased estimate for p, determined an unbiased estimate for p which is a function of T.

My attempt:

Clearly the sufficient statistic we are looking for is . If I denotes the indicator function, then we can see that is an unbiased estimator for p because .

So using Rao-Blackwell, we want to find

Now the pgf of is so the pgf of is

If we expand out that pgf using binomial expansion and consider the coefficient of , we find that

By replacing n with n-1 we easily get an expression for . And putting that into what we have above gives:

My problem is that this estimator should NOT depend on p but I don't see where I've gone wrong. There should be another p to cancel it out but I can't find where it should be! Any help would be greatly appreciated.
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#2
anything?
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7 years ago
#3
(Original post by lilman91)
anything?
I think the problem is on the line starting "Using Rao-Blackwell..". The conditional probability should be

0
#4
(Original post by Mark13)
I think the problem is on the line starting "Using Rao-Blackwell..". The conditional probability should be

oh haha - stupid! thanks
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