Variable selection in functional linear concurrent regression. Issue 3 (4th May 2020) - Ghosal, Rahul; Maity, Arnab; Clark, Timothy; Longo, Stefano B.
Summary: We propose a novel method for variable selection in functional linear concurrent regression. Our research is motivated by a fisheries footprint study where the goal is to identify important time‐varying sociostructural drivers influencing patterns of seafood consumption, and hence the fisheries footprint, over time, as well as estimating their dynamic effects. We develop a variable‐selection method in functional linear concurrent regression extending the classically used scalar‐on‐scalar variable‐selection methods like the lasso, smoothly clipped absolute deviation (SCAD) and minimax concave penalty (MCP). We show that in functional linear concurrent regression the variable‐selection problem can be addressed as a group lasso, and their natural extension: the group SCAD or a group MCP problem. Through simulations, we illustrate that our method, particularly with the group SCAD or group MCP, can pick out the relevant variables with high accuracy and has minuscule false positive and false negative rate even when data are observed sparsely, are contaminated with noise and the error process is highly non‐stationary. We also demonstrate two real data applications of our method in studies of dietary calcium absorption and fisheries footprint in the selection of influential time‐varying covariates.