root mean squared error of prediction

synonyms: root mean squared error of estimation, standard error of estimation, standard error of prediction
initialisms: RMSEP, RMSPE, SEP
https://doi.org/10.1351/goldbook.10110

In multivariate calibration or classification for \(N\) evaluation data where \(c_{i}\) is an observed value and \(\hat c_{i}\) is the predicted value \[E_{\rm{RMSEP}} = \sqrt {\frac{\sum\limits_{i\,=\,1}^{i\,=\,N} (\hat c_{i}\,-\,c_{i})^2}{N}}\]

Notes:
  1. RMSEP is related to the prediction error sum of squares (PRESS) by \(E_{\rm{RMSEP}} = \sqrt \frac{E_{\rm{PRESS}}}{N}\) .
  2. For completely independent, normally distributed evaluation data, RMSEP is a measure of the bias of the calibration.
  3. When prediction is by cross validation RMSEP may be termed root mean square error of cross validation.
Source:
PAC, 2016, 88, 407. (Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)) on page 424 [Terms] [Paper]