In chemometrics traditional calibration in case of spectral measurements express a quantity of interest (e.g. a concentration) as a linear combination of the spectral measurements at a number of wavelengths. Often the spectral measurements are performed at a large number of wavelengths and in this case the number of coefficients in the linear combination is magnitudes larger than the number of observations. Traditional approaches to handling this problem includes principal components, partial least squares, ridge regression, LASSO, and other shrinkage methods. As a continuous-wavelength alternative we suggest replacing the linear combination by an integral over the range of the wavelength of a unknown coefficient-function multiplied by the spectral measurements. We then approximate the unknown function by a linear combination of some basis functions, e.g. B-splines. The method is illustrated by an example in which the octane number of gasoline is related to near infrared spectral measurements. The performance is found to be much better that for the traditional calibration methods.
|Title of host publication||23. Symposium i Anvendt Statistik, Økonomisk Institut, Københavns Universitet / Danmarks Statistik|
|Publication status||Published - 2001|