Calibration with Absolute Shrinkage

In this paper, penalized regression using the L-1 norm on the estimated parameters is proposed for chemometric je calibration. The algorithm is of the lasso type, introduced by Tibshirani in 1996 as a linear regression method with bound on the absolute length of the parameters, but a modification is suggested to cope with the singular design matrix most often seen in chemometric calibration. Furthermore, the proposed algorithm may be generalized to all convex norms like Sigma/beta (j)/(gamma) where gamma greater than or equal to 1, i.e. a method that continuously varies from ridge regression to the lasso. The lasso is applied both directly as a calibration method and as a method to select important variables/wave lengths. It is demonstrated that the lasso algorithm, in general, leads to parameter estimates of which some are zero while others are quite large (compared to e.g. the traditional PLS or RR estimates). By using several benchmark data sets, it is shown that both the direct lasso method and the regression where the lasso acts as a wavelength selection method most often outperform the PLS and RR methods. Copyright (C) 2001 John Wiley & Sons, Ltd.