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.

偏最小二乘法在化学计量学的光谱预测中特别成功。通过将光谱数据视为随机过程的实现，可以应用功能偏最小二乘法。受从定向刨花板配料收集的光谱数据的启发，我们提出了函数偏最小二乘回归的稀疏版本。所提出的方法旨在实现函数偏最小二乘基的局部稀疏（即，某些子区域为零）估计，更重要的是，实现斜率函数的局部稀疏估计。新方法将函数正则化技术应用于函数偏最小二乘的每个迭代步骤，并实现了一种计算方法，该方法可识别估计斜率函数的非零子区域。