In this paper, penalized regression using the L-1 norm on the estimated par
ameters 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 chemo
metric 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 t
o 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 whic
h some are zero while others are quite large (compared to e.g. the traditio
nal 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 metho
ds. Copyright (C) 2001 John Wiley & Sons, Ltd.