SigFPLS: A Signatures‐Based Approach for Scalar‐on‐Function Regression Model

ABSTRACT

In functional data analysis, methods based on basis expansion are already well developed. However, when faced with collinearity in multivariate functional covariates, these methods may not perform effectively. In this paper, by using a new signature‐based method, we introduce a novel method within the scalar‐on‐function regression framework, leveraging signature method and partial least squares (PLS), which we call SigFPLS . This method outperforms traditional functional regression models and the signature‐based functional linear model by offering several key benefits: simple process for parameter tuning, easy implementation and effective handling of multicollinearity in multivariate functional data. Through extensive simulation studies and rigorous real data analysis, we demonstrate the effectiveness of our proposed method with focus on the scalar‐on‐function regression data, especially when dealing with multi‐dimensional and rough functional covariates.