RMSEP vs RMSECV vs RMSEC vs RMSEE I am getting real confused now, What is the difference between,
RMSEP (Root Mean Square Error of Prediction), RMSECV(Root Mean Square Error of Cross Validation), RMSEC  (Root Mean Square of Calibration), RMSEE (Root Mean Swuare Error of Estimation)
Are they the square root of their corresponding MSE*.
And what about PRESS (Prediction Residual Error Sum of Square)?
Need some help please!
 A: *

*yes, the R* (root...) versions are the square root of the corresponding MSEs (mean squared errors) 

*They differ in the type of cases that are used to measure them:


*

*RMSEC: calibration error, i.e. the residuals of the calibration data.
(R)MSEC measures goodness of fit between your data and the calibration model. 
Depending on the type of data, model and application this can be subject to a huge optimistic bias due to overfitting compared to the (R)MSE observed for real cases when applying the calibration. If the model suffers from not being complex enough (underfitting), calibration error approximates prediction error. But it cannot indicate overfitting. 

*RMSECV: errors are calculated on test/train splits using a cross validation scheme for the splitting.
If the splitting of the data is done correctly, this gives a good estimate on how the model built on the data set at hand performs for unknown cases. 
However, due to the resampling nature of the approach, it actually measures performance for unknown cases that were obtained among the calibration cases. I.e. it does not measure how well the model works for cases that are measured months after calibration is done. For that, you need

*MSEP/RMSEP: prediction error, i.e. measured on real cases and compared to reference values obtained for these.
RMSEP can measure e.g. how performance deteriorates over time (e.g. due to instrument drift), but only if the validation experiments have a design that allows to measure these influences. 
General remarks: 


*

*I'd recommend to report for both cross validation and prediction errors in detail how the test cases are set apart, and for what factors independence was ensured.
I regularly meet descriptions of "independent testing" (RMSEP) where acutally a single split of the calibration data was performed. 

*A one-time split of the data obtained for calibration typically yields no better performance estimate than a cross validation. I claim this because in practice, most data leaks occur just as easily for one split as for the many splits in cross validation. Nevertheless, it may be easier to implement a protocol that in practice avoids these errors in a very transparent way for predicition error
