# unbiased estimator

• Mar 19th 2008, 01:22 PM
kuntah
unbiased estimator
We have the test samples$\displaystyle X_{1},...,X_{n}$ from
$\displaystyle U(-\theta,\theta)$
with parameter $\displaystyle \theta$

Now show that $\displaystyle T = (3/n) (X^{2}_{1}+....+X^{2}_{n})$
is an unbiased estimator for $\displaystyle \theta^2$

My main problem is that I don't know which distribution this U stands for, is it the uniform distribution?

Can someone solve this plz
• Mar 20th 2008, 03:20 AM
CaptainBlack
Quote:

Originally Posted by kuntah
We have the test samples$\displaystyle X_{1},...,X_{n}$ from
$\displaystyle U(-\theta,\theta)$
with parameter $\displaystyle \theta$

Now show that $\displaystyle T = (3/n) (X^{2}_{1}+....+X^{2}_{n})$
is an unbiased estimator for $\displaystyle \theta^2$

My main problem is that I don't know which distribution this U stands for, is it the uniform distribution?

Can someone solve this plz

You need to show that:

$\displaystyle E(T) = \theta^2$

There are two ways of doing this both fairly easy. The first is to write out
the intgral and do it, the second is to remember that the expectation operator
is linear, so:

$\displaystyle E(T) = \frac{3}{n} ~\sum_{i=1}^n E(x_i^2)$

RonL