We present a new methodology for simultaneous variable selection and parameter estimation in function-on-scalar regression with an ultra-high dimensional predictor vector. We extend the LASSO to functional data in both the dense functional setting and the sparse functional setting. We provide theoretical guarantees which allow for an exponential number of predictor variables. Simulations are carried out which illustrate the methodology and compare the sparse/functional methods. Using the Framingham Heart Study, we demonstrate how our tools can be used in genome-wide association studies, finding a number of genetic mutations which affect blood pressure and are therefore important for cardiovascular health.
"The function-on-scalar LASSO with applications to longitudinal GWAS." Electron. J. Statist. 11 (1) 1351 - 1389, 2017. https://doi.org/10.1214/17-EJS1260