Distribution of the statistic?

[yhp266]

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

 

[yhp266]

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

 

[ssd]

1/I don't 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.