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

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.

Classification of multivariate functional data on different domains with Partial Least Squares approaches

“…Technical arguments on the PLS methods are given. The finite sample performance of the regression and classification models are assessed by simulations and real data (EEG, Ozone, wafer,...) applications where we compare the proposed methods with some benchmarks, in particular a PLS regression model of the literature (Beyaztas and Shang (2022)) and well known principal components regression and some machine learning models.…”

“…We extend the recent contribution in Beyaztas and Shang (2022) by investigating more exhaustively PLS procedures, in particular, we derive the relationship between the PLS regression with univariate functional data (FPLS) and the PLS regression with multivariate functional data (MFPLS). From a computational point of view, this relationship provides an alternative way to estimate the PLS components for multivariate functional data from the corresponding univariate ones.…”

“…, d. Then, they extract new uncorrelated features based on linear combinations of the obtained PLS components. In Beyaztas and Shang (2022) the aim is to provide a robust version of PLS for multivariate functional data. They have extended Aguilera et al (2010) basis expansion results on multivariate functional data and proposed a partial robust M-regression in this framework.…”

Density kernel depth for outlier detection in functional data

“…Not dealing with outliers can affect the statistical analysis, leading to biased and inconsistent results. For instance, in a functional regression model the least squares estimator may not be reliable, when outliers are present in the data [5].…”

On partial least‐squares estimation in scalar‐on‐function regression models

“…In this study, our focus is restricted to the scalar‐on‐function regression model (SoFRM), which investigates the functional relationship between a scalar response and functional predictor variables. SoFRM has received significant attention in the literature and has been successfully applied in many fields, such as bioscience, meteorology, chemometrics, and engineering (see, e.g., previous studies 1,3,6–13 ).…”