1. ## Re: Variance estimation

Originally Posted by Masteras
for n=2 the have the same variance the V and .
Z=X-Y~N(0,2*sigma^2). from theory, we know it.
From which theory? Are you using mgf for transformation?

Transformations for W=Z^2 to end up with a gamma. The U=W/a (where a=2sigma^2) to see what kind of a gamma is this (chi-square actually). I told you to take it step by step to understand. keep in mind that the variance of your V (for n=2) is 2sigma^4, the same.
I am sure you have something interesting but I can't follow you. It's easier to see when you actually write some mathematical arguments rather than "keep in mind that the variance of your V (for n=2) is 2sigma^4, the same"

2. ## Re: Variance estimation

Here is the theory.

If are independent, standard normal random variables then the sum of their squares will follow chi-square distribution with k degrees of freedom.

A random variable can be standardised. Since we have then we also have

which are standard normal random variables and the sum of their square will follow chi-square distribution. It follows from this that ~; and

A bit of algebra and you get

3. ## Re: Variance estimation

let's see.
, since they are iid variables. .
The distribution of this Z is a . The variance of a is .

4. ## Re: Variance estimation

BGM in this post also thinks variance for is higher.
http://talkstats.com/showpost.php?p=40161&postcount=9

Anyway, thanks for your replies but I can't see why variances for two estimators are the same.

5. ## Re: Variance estimation

Since you opu it this way, take BGM's 1st hint in that post and work the distribution of V, construct V from the first hint. The distribution is a . The variance of this is ...

6. ## Re: Variance estimation

Originally Posted by _joey
I think I've solved it. I should write I used your idea to solve the problem. and where n=2

I've got a quick question: is there an easy way to show ?

Err I mean for n, not just n=2.
The generalization is

Is that what you want?

7. ## Re: Variance estimation

The proof of general form. I will search books.google.com