连续谱数据的函数型主成分回归

对连续谱数据不做离散化处理，而是将光滑后的连续谱作为连续曲线，进行函数型主成分回归分析，以期获得既可降维又能减少信息损失的回归方程.在此建模过程中，还引入连续谱的导数曲线作为协变量，并给出函数型主成分回归系数的bootstrap置信区间.作为实证研究，对玻璃样品的X射线谱和样品中硅元素含量进行回归分析.研究结果表明，基于函数型主成分的回归分析对响应变量具有较强解释能力，同时其回归系数更加符合数据本身的特点，显示出新方法所具有的优越性与实用价值. 

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.