New approaches for scalar-on-function regression via independent component analysis

This is the authors' abstract. We don't add key points for this paper.

Scalar-on-function regression aims to explain a scalar response variable using a functional predictor whose observations are curves. To address the problem of estimating this model from discrete observations of the curves, several methods have been proposed in the literature, most commonly based on representing the curves with function bases and performing regression on the corresponding basis coefficients (scores). When the basis is not estimated from the data, the basis coefficients are often highly correlated, and data-driven bases, such as those associated with principal component analysis or partial least squares, have been considered. In this work, we propose a completely new methodology based on extracting independent components from the curves to be used as predictors. Various Monte Carlo simulation studies have been conducted to demonstrate its good practical performance compared to functional principal component regression (FPCR) and functional partial least squares regression (FPLSR). Finally, an application using data from the electronics industry highlights the ability of the proposed estimation methods to accurately interpret the relationship between the scalar response variable and the functional predictor.