Calibration with nearcontinuous spectral measurements 
Henrik Aalborg Nielsen, Michael Rasmussen, Henrik Madsen

Abstract  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
continuouswavelength alternative we suggest replacing the linear
combination by an integral over the range of the wavelength of a
unknown coefficientfunction multiplied by the spectral measurements.
We then approximate the unknown function by a linear combination of
some basis functions, e.g. Bsplines. 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. 
Keywords  Spectra; spline; PLS; PCR 
Type  Conference paper [Without referee] 
Conference  23. Symposium i Anvendt Statistik 
Editors  NielsErik Jensen og Peter Linde 
Year  2001 Month January pp. 255264 
Publisher  Økonomisk Institut, Københavns Universitet / Danmarks Statistik 
ISBN / ISSN  8750111515 
BibTeX data  [bibtex] 
IMM Group(s)  Mathematical Statistics 