Semi-Parametric Estimation in the Compositional Modeling of Multicomponent Systems from Raman Spectroscopic Data

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Identification and quantification of molecular species are central applications of molecular spectroscopy. In complex multicomponent systems like tissue samples, linear parametric models are often used to estimate the relative concentrations of the biochemical components of the sample. In situations where not all of the components of the sample are known or modeled, such parametric models can suffer from omitted variable bias and result in skewed estimates of component concentrations. We propose a semi-parametric approach that tries to avoid this omitted variable bias by effectively including unknown covariates as a non-parametric term in the regression equation. Constituent concentrations estimated with such partial linear models should outperform strict parametric linear models when the user has limited information on the composition of a multi-constituent system.