Using basis expansions for estimating functional PLS regression Applications with chemometric data
Using basis expansions for estimating functional PLS regression Applications with chemometric data
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DOI：
10.1016/j.chemolab.2010.09.007
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发表时间：
2010-12-15
影响因子：
3.9
通讯作者：
Saporta, Gilbert
中科院分区：
文献类型：
--
作者：
Aguilera, Ana M.;Escabias, Manuel;Saporta, Gilbert
有许多化学计量学的应用，如光谱学，其目的是解释一个函数变量（光谱）的标量响应，其观测值是波长的函数，而不是矢量。本文研究了预测变量为函数型随机变量时线性模型的偏最小二乘回归估计问题。由于预测观测值所属的空间的无限维，它们通常由函数基所跨越的有限维空间内的曲线/函数来近似。我们表明，PLS回归与功能预测是等价的有限多元PLS回归使用扩展基系数作为预测，在这个意义上说，在PLS迭代的每一步，得到相同的预测。此外，从使用基系数估计的线性模型，我们推导出的回归系数函数的PLS估计的表达式从模型与功能预测。通过这种功能PLS方法提供的结果进行了比较与功能PCR和离散PLS和PCR使用不同的模拟和光谱数据集。(C)2010爱思唯尔有限公司版权所有。
There are many chemometric applications, such as spectroscopy, where the objective is to explain a scalar response from a functional variable (the spectrum) whose observations are functions of wavelengths rather than vectors. In this paper, PLS regression is considered for estimating the linear model when the predictor is a functional random variable. Due to the infinite dimension of the space to which the predictor observations belong, they are usually approximated by curves/functions within a finite dimensional space spanned by a basis of functions. We show that PLS regression with a functional predictor is equivalent to finite multivariate PLS regression using expansion basis coefficients as the predictor, in the sense that, at each step of the PLS iteration, the same prediction is obtained. In addition, from the linear model estimated using the basis coefficients, we derive the expression of the PLS estimate of the regression coefficient function from the model with a functional predictor. The results provided by this functional PLS approach are compared with those given by functional PCR and discrete PLS and PCR using different sets of simulated and spectrometric data. (C) 2010 Elsevier B.V. All rights reserved.