Modeling and analysis of spectroscopy data is an active area of research with applications to chemistry and biology. This paper focuses on modelling high-dimensional spectra for the purpose of noise reduction and prediction in problems where the spectra can be used as covariates. We propose a functional representation of the spectra as well as functional regression model that accommodates multiple spatial dimensions. Both steps emphasize sparsity to reduce the number of parameters and mitigate over-fitting. The motivating application for these models, discussed in some detail, is predicting bone-mineral-density (BMD), an important indicator of fracture healing, from Raman spectra, in both the in vivo and ex vivo settings of a bone fracture healing experiment. To illustrate the general applicability of the method, we also use it to predict lipoprotein concentrations from spectra obtained by nuclear magnetic resonance (NMR) spectroscopy.
"Structured regression models for high-dimensional spatial spectroscopy data." Electron. J. Statist. 11 (2) 4151 - 4178, 2017. https://doi.org/10.1214/17-EJS1301