A new formulation to estimate the variance of model prediction. Application to near infrared spectroscopy calibration.

Evaluation of uncertainty affecting predictions is a major trend in analytical chemistry and chemometrics. Several approximate expressions and resampling methods have been proposed for the estimation of prediction uncertainty when using multivariate calibration. This article proposes a new expression for the variance of prediction, adapted to near infrared spectroscopy specificities and particularly to the spectral error structure, induced by the high colinearity of the variables. The proposed analytical expression enables a detailed evaluation of the different contributions and components of uncertainty affecting the model. An application to real data of feedstuff near infrared spectra related to protein content has shown its advantages.