What is the point of using predicted residual sum of squares (PRESS) instead of root-mean-squared-error-of-cross-validation(RMSECV)? In many books, especially in the area of chemometrics, the authors mention PRESS for CV scenarios.
For parameter tuning such as number of LVs in PLS regression or lambda in ridge regression, RMSECV makes a lot more sense to me, since the results at least provide me some insight about the approximate performance of the final model whereas PRESS is just an arbitrary number.
I can only think of a single reason which is PLS2 in which there are multiple response variables to be predicted and a single parameter to be tuned.
Therefore, my question is: Is there a statistical or any other use of PRESS that I am not aware of?