Smooth LASSO estimator for the Function-on-Function linear regression model

A new estimator, named S-LASSO, is proposed for the coefficient function of Function-on-Function linear regression model. The S-LASSO estimator shown to be able increase interpretability model, by better locating regions where zero, and smoothly estimate non-zero values function. sparsity ensured a \textit{functional LASSO penalty}, which pointwise shrinks toward zero function, while smoothness provided two roughness penalties that penalize curvature final estimator. resulting proved estimation sign consistent. Via an extensive Monte Carlo simulation study, predictive performance are than (or at worst comparable with) competing estimators already presented in literature before. Practical advantages illustrated through analysis \textit{Canadian weather}, \textit{Swedish mortality} \textit{ship CO\textsubscript{2} emission data}. method implemented \textsf{R} package \textsf{slasso}, openly available online on CRAN.