I have shown that the expected value of $\displaystyle \delta (x)$ is $\displaystyle \theta+1$

How possibly can $\displaystyle \delta (x)$ be an consistent estimator?

Thanks!

casper

Printable View

- Dec 1st 2010, 11:44 AMcasperychow do i show this is a consistent estimator?
I have shown that the expected value of $\displaystyle \delta (x)$ is $\displaystyle \theta+1$

How possibly can $\displaystyle \delta (x)$ be an consistent estimator?

Thanks!

casper - Dec 3rd 2010, 04:27 PMmatheagle
$\displaystyle P\left(\left|\hat\theta-\theta\right|>\epsilon\right)= {1\over n} \to 0$

while $\displaystyle E\left(\hat\theta-\theta\right)^2=(n)^2{1\over n}+0\left(1-{1\over n}\right)=n\to \infty$