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Distribution of the statistic? 
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#1
May1608, 05:14 AM

P: 6

Hi all, I've been confused about this for a while. Since it wasn't mentioned in class or my textbook, it probably reflects a fundamental lack of understanding :(
With any unbiased estimator, why is the distribution of the estimates also the distribution of the statistic? Eg, suppose we have 5 independent and identically distributed normal random variables with variance 1 and mean (unknown parameter). We observe some numbers say { 4, 5, 2 ,7 , 12}. and we use sample mean as the estimator for mean. The sample mean is clearly normally distributed. But why is this also the distribution for mean 


#2
May1608, 06:11 AM

P: 6

And is it possible to have 2 different unbiased estimators for the same parameter?
Wouldnt it not make sense to have multiple distributions of estimates for a particular parameter 


#3
May1608, 01:01 PM

P: 239

1/I dont understand your first question.
2/Yes, many unbiased estimators for one parameter is possible. Let x1,x2,...,xn be a sample form N(mu,sigma). Then sample mean or any xi is unbiased for mu but the have different distributions. Look up what is ment by MVUE. 


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