how do i show this is a consistent estimator?

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December 1st 2010, 11:44 AM
casperyc

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how do i show this is a consistent estimator?

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

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

Thanks!

casper
December 3rd 2010, 04:27 PM
matheagle

$P\left(\left|\hat\theta-\theta\right|>\epsilon\right)= {1\over n} \to 0$

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

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