Parallel calibration revisited: The second direction for shrinkage estimation of regression coefficients can be as natural and necessary as the traditional one

In the traditional framework of multivariate spectroscopic calibration, the most popular method, partial least squares (PLS), shrinks the regression coefficients based on the information of training sample concentrations. Motivated by the concept of parallel calibration, the second direction for shrinkage of regression coefficients, the direction towards unknown sample spectra is investigated in this paper. A different multivariate calibration method, parallel calibration model based on partial least squares, PCPLS is proposed. With both theoretical support and analysis of some real data sets, it is demonstrated that the second shrinkage direction is at least as natural and necessary as the traditional one. An interesting difference of the proposed method from traditional methods is the involvement of unknown sample spectra and consideration of their error in the training process. Some new related problems and potential applications of this method are also briefly discussed.