2ND-DERIVATIVE FUNCTIONAL REGRESSION WITH APPLICATIONS TO NEAR-INFRARED SPECTROSCOPY

A linear regression method to predict a scalar from a discretized smoo th function is presented. The method takes into account the functional nature of the predictors and the importance of the second derivative in spectroscopic applications. This motivates a functional inner produ ct that can be used as a roughness penalty. Using this inner product, we derive a linear prediction method that is similar to ridge regressi on but with different shrinkage characteristics. We describe its pract ical implementation and we address the problem of computing the second derivatives nonparametrically. We apply the method to a calibration e xample using near infra-red spectra. We conclude with a discussion com paring our approach with other regression algorithms.