An adaptive functional regression framework for locally heterogeneous signals in spectroscopy

In recent years, there has been growing attention towards food nutritional properties, traceability, and production systems prioritizing environmental sustainability. Consequently, there is a rising demand for tools evaluating food quality and authenticity, with mid-infrared (MIR) spectroscopy techniques playing a pivotal role to collect vast amounts of data. These data pose some challenges that existing methods struggle to address, thus necessitating the development of new statistical techniques. We introduce an adaptive functional regression framework allowing for the definition of a flexible estimator accommodating different degrees of smoothness. We provide an optimization procedure handling both Gaussian and non-Gaussian responses, and allowing for the inclusion of scalar covariates. Our proposal is applied to MIR spectroscopy data, providing excellent performances when predicting milk composition and cows' dietary regimens. Furthermore, the developed inferential routine enhances the interpretability of the results, providing valuable insights leading to a deeper understanding of the relation between specific wavenumbers and milk characteristics.