A Robust Functional Partial Least Squares for Scalar-on-Multiple-Function Regression

TL;DR

This paper introduces a robust functional partial least squares method for scalar-on-multiple-function regression, effectively handling outliers and improving estimation reliability in datasets with contaminated data.

Contribution

It develops a robust estimation approach using partial robust M-regression within the functional partial least squares framework, addressing outlier sensitivity in scalar-on-multiple-function regression.

Findings

The proposed method outperforms classical PLS and PCA methods in robustness.

Monte Carlo experiments demonstrate improved estimation accuracy.

Application to chemometric datasets shows better predictive performance.

Abstract

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.