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March 8th, 2012, 09:00 AM   #1
Joined: Feb 2012

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bias estimator

Before the election, a polling firm asked 1,000 people and an another poll firm asks
2000 (other) people about what they did vote. A newspaper proposes to take the mean of the Labour Party's average level of support
of the two measurements as an estimate of the true level of support to the party.

Show that this is an bias of an estimator.
Why is this not optimal?
Suggest a better estimator.
PerMortenIvar is offline  
March 8th, 2012, 12:14 PM   #2
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Re: bias estimator

so see that this estimator is unbiased you need to compute its expectation (easy). to see why it is not optimal you need to calculate its variance. I suggest you calculate the variance of a more general estimator, namely a*I1+b*I2 where a+b=1 a>0 b>0 and I1 and I2 are the results of the two polls. You'll see that ther is e unique choice of a (and b=1-a) that minimizes the variance, and it is not 1/2,1/2.
mehoul is offline  

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