Pareto calibration with built-in wavelength selection

In multivariate regression, it is often reported that wavelength selection can improve results. Improvement is often solely based on bias measures such as the root mean square error of calibration (RMSEC) and root mean square error of validation (RMSEV), R^2 for the calibration and validation, etc. In recent studies, it has been shown that when variance measures are included, Pareto optimal models can be determined. However, variance measures used to date do not provide the ability to choose wavelength subset models relative to full wavelength models when wavelength subset models may be the Pareto models. In this paper, simplex optimization is used with a more complete variance measure to generate Pareto optimal models. The standard basis set is used as well a basis set that includes the range and null space of the calibration spectra. Results show that it is possible to identify Pareto optimal models and if a wavelength subset is best, these are the models found. Regression coefficients for non-essential wavelengths are zero to near zero.