Adaptive function-on-scalar regression with a smoothing elastic net

This paper presents a new methodology, called AFSSEN, to simultaneously select significant predictors and produce smooth estimates in high-dimensional function-on-scalar linear model with sub-Gaussian errors. Outcomes are assumed lie general real separable Hilbert space, H, while parameters subspace known as Cameron–Martin K, which closely related Reproducing Kernel Spaces, so that the parameter inherit particular properties, such smoothness or periodicity, without enforcing properties on data. We propose regularization method style of an adaptive Elastic Net penalty involves mixing two types functional norms, providing fine tune control both smoothing variable selection estimated model. Asymptotic theory is provided form oracle property, concludes simulation study demonstrating advantages using AFSSEN over existing methods terms prediction error selection.