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Generalized signed-rank estimation and selection for the functional linear model

ABSTRACT The increased capability to record and store data has revolutionized the way in which such data are analysed. This development has led to the need to have robust variable selection methods that effectively select relevant and important variables in the formulation of a predictive model. The process of data reduction through variable selection is an important aspect in many fields, and even so in functional data analysis. This involves analysing high-dimensional data objects, sometimes in the presence of outliers, therefore creating the need for a robust variable selection method that effectively identifies a subset of significant predictors that can be used to model functional data. The proposed signed-rank method improves the overall estimation and interpretability of the functional linear model. Asymptotic properties of the estimator are presented, as well as an extensive simulation study and application of the proposed approach to real-world data.