论文标题
一个强大的功能性局部最小二乘，用于标量 - 官能功能回归
A Robust Functional Partial Least Squares for Scalar-on-Multiple-Function Regression
论文作者
论文摘要
标量功能回归模型已成为探索标量响应与多个功能预测因子之间关系的流行分析工具。估计该模型的大多数现有方法都是基于最小二乘估计器，这些估计量可能会受到经验数据集中离群值的严重影响。当数据中存在异常值时，众所周知，基于最小二乘的估计值可能不会可靠。本文提出了一种鲁棒的功能部分最小二乘法，可以在标量 - 跨性功能回归模型中对回归系数进行稳健的估计。在我们的方法中，功能性部分最小二乘组件是通过部分稳健的M回归计算的。使用多个蒙特卡洛实验和两个化学计量数据集评估所提出方法的预测性能：葡萄糖浓度光谱数据和糖过程数据。通过提出的方法产生的结果与某些经典功能或多元部分最小二乘和功能性主成分分析方法进行了有利的比较。
The scalar-on-function regression model has become a popular analysis tool to explore the relationship between a scalar response and multiple functional predictors. Most of the existing approaches to estimate this model are based on the least-squares estimator, which can be seriously affected by outliers in empirical datasets. When outliers are present in the data, it is known that the least-squares-based estimates may not be reliable. This paper proposes a robust functional partial least squares method, allowing a robust estimate of the regression coefficients in a scalar-on-multiple-function regression model. In our method, the functional partial least squares components are computed via the partial robust M-regression. The predictive performance of the proposed method is evaluated using several Monte Carlo experiments and two chemometric datasets: glucose concentration spectrometric data and sugar process data. The results produced by the proposed method are compared favorably with some of the classical functional or multivariate partial least squares and functional principal component analysis methods.
