A robust functional partial least squares for scalar‐on‐multiple‐function regression

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. A robust functional partial least squares method is proposed to estimate the coefficients in the scalar‐on‐multiple‐function regression model robustly. In the proposed method, a data‐driven tuning parameter selection approach is used to determine the optimum tuning parameter and to achieve the desired robustness level without sacrificing efficiency. Monte Carlo experiments and empirical data analyses reveal that the proposed method produces superior estimation and predictive performance over the existing methods.