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March 8th, 2012, 10:00 AM  #1 
Newbie Joined: Feb 2012 Posts: 18 Thanks: 0  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. questions: Show that this is an bias of an estimator. Why is this not optimal? Suggest a better estimator. 
March 8th, 2012, 01:14 PM  #2 
Senior Member Joined: Feb 2012 Posts: 144 Thanks: 16  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=1a) that minimizes the variance, and it is not 1/2,1/2.


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