Bias is defined as an average of all errors (without abs) and this is, IMO, what I want.
However, I have been asked to give MEAN ERROR. Is this the same than bias and is it wrong to call bias as mean error?
Just in case I’m messing these definitions totally, description what I try to do:
Positions are forecasted and compared to absolute values. To give the error, RMSE and BIAS are calculated.
Best Answer
Very briefly, the MSE is the second moment of the bias. Let $\hat{\theta}$ be an estimator for the true quantity $\theta$. Then we have that
$Bias_\theta(\hat{\theta})=E(\hat{\theta})-\theta=E(\hat{\theta}-\theta)$
while
$MSE_\theta(\hat{\theta)} = E((\hat{\theta}-\theta)^2)$ and $RMSE \equiv \sqrt(MSE)$.