Robust functional linear regression models

Abstract

With advancements in technology and data storage, the availability of functional data whose sample observations are recorded over a continuum, such as time, wavelength, space grids, and depth, progressively increases in almost all scientific branches. The functional linear regression models, including scalar-on-function and function-on-function, have become popular tools for exploring the functional relationships between the scalar response-functional predictors and functional responsefunctional predictors, respectively. However, most existing estimation strategies are based on nonrobust estimators that are seriously hindered by outlying observations, which are common in applied research. In the case of outliers, the non-robust methods lead to undesirable estimation and prediction results. Using a readily-available R package robflreg, this paper presents several robust methods build upon the functional principal component analysis for modeling and predicting scalar-on-function and function-on-function regression models in the presence of outliers. The methods are demonstrated via simulated and empirical datasets.