Multivariate calibration with single-index signal regression

In general, linearity is assumed to hold in multivariate calibration, but this may not be true. Penalized signal regression can be extended with an explicit link function between linear prediction and response, in the spirit of single-index models. Like the vector of calibration coefficients, the unknown link function is being estimated by P-splines. Application to simulations and three data sets shows that if a non-linearity is present, it will be picked up by the model and prediction will be improved.