Multivariate calibration on heterogeneous samples.

Data heterogeneity has become a challenging problem in modern data analysis. Classic statistical modeling methods, which assume the data are independent and identically distributed, often show unsatisfactory performance on heterogeneous data. This work is motivated by a multivariate calibration problem from a soil characterization study, where the samples were collected from five different locations. Newly proposed and existing signal regression models are applied to the multivariate calibration problem, where the models are adapted to handle such spatially clustered structure. When compared to a variety of other methods, e.g. kernel ridge regression, random forests, and partial least squares, we find that our newly proposed varying-coefficient signal regression model is highly competitive, often out-performing the other methods, in terms of external prediction error. • We propose a new varying-coefficient signal regression approach that outperforms several other Multivariate Calibration approaches. • We model clustered or spatial data ito improve performance based on external prediction error. • We overview Penalized Signal Regression, then propose a new extension. • We use a rich spectral dataset soil samples from four U.S. states and the country of France and provide a combined analysis. • Our methods aim for the dual role of quality external prediction and interpretability through statistical models. [ABSTRACT FROM AUTHOR]