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February 7th, 2010, 12:44 PM  #1  
Member Joined: Sep 2008 Posts: 41 Thanks: 0  Unbiased estimator proof
First, here's the question: Quote:
. It seems "too easy" this way, which is what makes me think this isnt correct. Even though this is an odd numbered question in my book, there is no answer for it. Maybe the authors thought it was "trivial". Thanks for any help  
February 7th, 2010, 01:29 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,581 Thanks: 610  Re: Unbiased estimator proof
So it's easy! What's wrong with that?? It happens to be correct. A more interesting problem is to show that if you use the sample mean rather than the true mean, you have to change the divisor from n to n1. 
February 7th, 2010, 01:45 PM  #3 
Member Joined: Sep 2008 Posts: 41 Thanks: 0  Re: Unbiased estimator proof
Hi mathman, Actually, the reasoning for dividing by n1 instead of n in the definition of sample variance S^2 is a few pages before these exercises! It was shown that this is done to make S^2 an unbiased estimator of population variance. My main concern about my proof above was that I knew (from a theorem) that , as well as other linear combinations like . But I wasnt sure if this was true for more "complicated" things like being equivalent to . As I said, there is a theorem for the first of those equations, but I cant find one for the last equation. It seems logical, but I just wanted to confirm that this sort of property always holds for similar expressions. Thanks! 
February 8th, 2010, 01:40 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,581 Thanks: 610  Re: Unbiased estimator proof
The average of a finite sum is always the sum of the averages, no matter what the terms look like.

February 8th, 2010, 01:48 PM  #5 
Member Joined: Sep 2008 Posts: 41 Thanks: 0  Re: Unbiased estimator proof
Yeah, I started thinking about that after I first replied. There isnt anything special about whether its simple X or a function of X, its still just the sum of them. Thanks! 
November 10th, 2012, 01:50 AM  #6 
Newbie Joined: Nov 2012 Posts: 2 Thanks: 0  Re: Unbiased estimator proof
The proof as a whole can be found under http://economictheoryblog.wordpress.com ... exlatexs2/ Regards 
November 10th, 2012, 06:51 PM  #7  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,103 Thanks: 907  Re: Unbiased estimator proof Quote:
Ce post date de: Sun Feb 07, 2010 4:44 pm  
September 12th, 2014, 12:59 AM  #8 
Newbie Joined: Nov 2012 Posts: 2 Thanks: 0  

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