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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'mean square error'
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The bias is squared in the second equation by gh0st
Correction id: 7485
Filed on: 2006-01-31 09:28:14
Status: Accepted on 2006-01-31 12:50:26
Type: Erratum
Correction text:
A square is missing in the second equation for the mean square error:
$MSE(\hat{\theta})=Var(\hat{\theta})+Bias^{2}(\hat{\theta})$ .
Justification: $Bias(\hat{\theta}):=E(\hat{\theta})-\theta$, so that
$MSE(\hat{\theta})=E[(\hat{\theta}-\theta)^{2}]=E\left[\left((\hat{\theta}-E[\hat{\theta}])+
(E[\hat{\theta}]-\theta)\right)^{2}\right]=Var(\hat{\theta})+2(E[\hat{\theta}]-\theta)E[(\ha
t{\theta}-E[\hat{\theta}])]+E\left[\left(E[\hat{\theta}]-\theta\right)^{2}\right]=Var(\hat{\
theta})+Bias^{2}(\hat{\theta})$ |
No comment from object owner CWoo.
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