Selecting the derivative of a functional covariate in scalar-on-function regression

This paper presents tests to formally choose between regression models using different derivatives of a functional covariate in scalar-on-function regression. We demonstrate that for linear regression, can be nested within model includes point-impact effects at the end-points observed functions. Contrasts then employed test specification derivatives. When nonlinear are employed, we apply C determine statistical significance structure and scalar response. The finite-sample performance these methods is verified simulation, their practical application demonstrated both chemometric environmental data sets.