IMPROVED PREDICTION ERROR-ESTIMATES FOR MULTIVARIATE CALIBRATION BY CORRECTING FOR THE MEASUREMENT ERROR IN THE REFERENCE VALUES

The validation of multivariate calibration models using measured refer ence values leads to a so-called apparent prediction error estimate, w hich is systematically larger than the true prediction error, The reas on for this difference is clear: the measured reference values contain an irrelevant random component, the measurement error, which cannot b e predicted by any model, not even the ''true'' one. However, the cont ribution of the measurement error in the reference values to the appar ent prediction error estimate is interpreted as an inadequacy of the c alibration model rather than an inadequacy of the reference values the mselves. This phenomenon of confounding has been pointed out recently by several researchers, but no generally applicable solution was given . In this paper we propose a simple correction procedure that yields a more realistic estimate of the true prediction error. A large potenti al improvement over the conventional estimate is demonstrated for a va riety of applications taken from the literature.