Functional principal component regression for continuous spectra data

The method treating the smooth spectra as functional data was proposed and regression analysis was carried out based on functional principal components of spectra curves to obtain regression models without discretization. In modeling, the derivative curves of spectra can be introduced and bootstrap confidence intervals for functional coefficients were obtained. Using this method, the regression relationship between element concentration and X-ray spectra of glass samples was analyzed. It is shown that the functional regression based on principal components is more acceptable and has many advantages, because it complies with the characteristics of the data itself while attaining strong explanatory ability.