High dimensional variable selection through group Lasso for multiple function‐on‐function linear regression: A case study in PM10 monitoring

Analyzing the effect of chemical and local meteorological variables over the behaviour in PM10$$ {\mathrm{PM}}_{10} $$ concentrations in the Abruzzo region (Italy), with the objective of forecasting and controlling air quality, motivates the current work. Given that the available data are curves that represent the day‐to‐day variations, a multiple function‐on‐function linear regression (MFFLR) model is considered. By assuming the Karhunen‐Loève expansion, MFFLR model can be reduced to a classical linear regression model for each principal component of the functional response in terms of all principal components (PCs) of the functional predictors. In this sense, a regularization approach for functional principal component regression based on the merge of functional data analysis with group Lasso is proposed. This novel methodology allows to estimate the model and, simultaneously, select those relevant functional predictors with the functional response, where each functional independent variable is represented by a group of input variables derived by the PCs.