Sparse functional partial least squares regression with a locally sparse slope function

The partial least squares approach has been particularly successful in spectrometric prediction in chemometrics. By treating the spectral data as realizations of a stochastic process, the functional partial least squares can be applied. Motivated by the spectral data collected from oriented strand board furnish, we propose a sparse version of the functional partial least squares regression. The proposed method aims at achieving locally sparse (i.e., zero on certain sub-regions) estimates for the functional partial least squares bases, and more importantly, the locally sparse estimate for the slope function. The new approach applies a functional regularization technique to each iteration step of the functional partial least squares and implements a computational method that identifies nonzero sub-regions on which the slope function is estimated. We illustrate the proposed method with simulation studies and two applications on the oriented strand board furnish data and the particulate matter emissions data.