Cross Validated Asked by Tiago Dias on January 1, 2022
I would like to understand the difference between Root Mean Squared Error and the Standard Prediction Error.
The SEP formula is simillar to the RMSE, but with an aditional term called bias inside the root squared.
Is expected to give similar values for my model?
$$RMSE = sqrt {{sum_{i=1}^n(y_i -hat y_i)^2} over n}$$
$$SEP = sqrt {{sum_{i=1}^n(y_i -hat y_i-bias)^2} over {n-1}}$$
$$bias = {{sum_{i=1}^n(y_i -hat y_i)} over n} $$
SEP functions similarly to RMSE, but the bias term acts to adjust the mean of the predictions to match the mean of the actuals. That is, if you were to add a constant term to all of your predictions, you would degrade your RMSE would would not affect your SEP.
Another way to express SEP is:
$$ SEP(y, hat{y}) equiv RMSE(y, hat{y} + bar{y} - bar{hat{y}}) $$
I can think of a few cases where predicting the mean accurately is less relevant and you might prefer a metric like SEP:
Answered by Dex Groves on January 1, 2022
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