  Calibration and prediction for NIR spectroscopy data are performed based on a
functional interpretation of the Beer-Lambert formula. Considering that, for
each chemical sample, the resulting spectrum is a continuous curve obtained as
the summation of overlapped absorption spectra from each analyte plus a
Gaussian error, we assume that each individual spectrum can be expanded as a
linear combination of B-splines basis. Calibration is then performed using two
procedures for estimating the individual analytes curves: basis smoothing and
smoothing splines. Prediction is done by minimizing the square error of
prediction. To assess the variance of the predicted values, we use a
leave-one-out jackknife technique. Departures from the standard error models
are discussed through a simulation study, in particular, how correlated errors
impact on the calibration step and consequently on the analytes' concentration
prediction. Finally, the performance of our methodology is demonstrated through
the analysis of two publicly available datasets.
