Statistics- unbiased estimator #3


by Roni1985
Tags: estimator, statistics, unbiased
Roni1985
Roni1985 is offline
#1
Mar1-10, 06:37 PM
P: 202
1. The problem statement, all variables and given/known data

Suppose that n=5 observations are taken from the uniform pdf, fY=1/[tex]\Theta[/tex] 0<y<[tex]\Theta[/tex]
where [tex]\Theta[/tex] is unknown. Two unbiased estimators for [tex]\Theta[/tex] are

[tex]\Theta[/tex]1= (6/5)*Ymax
[tex]\Theta[/tex]2= (6)*Ymin

which estimator would be better to use? hint: What must be true of Var(Ymax) and Var(Ymin) given that fy is symmetric ? Does your answer as to which estimator is better make sense on intuitive grounds ? Explain.


2. Relevant equations

Var(Y)=E[Y2] - E[Y]2

Ymin=n*(1-FY(y))n-1fY(y)

Ymax=n*(FY(y))n-1fY(y)

3. The attempt at a solution

I'm trying to calculate the variances of both the estimators and see which one is smaller.
But, there is the extra information like, n=5 and that the distribution is symmetric, and I'm sure I need to use it.
Plus, I don't know how to answer it on intuitive grounds.
Would appreciate any help.
Thanks.

EDIT:

Now, I am still trying to solve it, and if I know that the distribution is symmetric, the variance of Ymin and Ymax are the same.
However, since the first estimator is divided by 5, we know that it's 1/25 of the variance of the second estimator.
Can I say this ? Is this the"on intuitive grounds" answer that they are asking ?
What about the sample size n=5 ? what do I do with it ?

Thanks
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Roni1985
Roni1985 is offline
#2
Mar1-10, 08:38 PM
P: 202
anybody ?

can't figure it out :\


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