Investigating the link between $$\hbox {PM}_{2.5}$$ and atmospheric profile variables via penalized functional quantile regression

Fine particulate matter (\(\hbox {PM}_{2.5}\)) events negatively affect the health of numerous persons globally each year. Previous works have described the association between air pollution and surface-level meteorological conditions; however, there has been less focus on the task of linking air pollution events with meteorological conditions at higher levels of the atmosphere. Working within the functional data framework, we develop a penalized functional quantile regression (PFQR) procedure to model conditional quantiles of a continuous response based on a functional covariate, with the ability to penalize selected derivatives of the estimated coefficient function. Our aim is to investigate the relationship between atmospheric profile variables (APVs), assumed to be functional, and key quantiles of the conditional distribution of surface-level \(\hbox {PM}_{2.5}\). Via a simulation study, we find that the performance of our PFQR procedure compares favorably to other related approaches. We conclude with an analysis of \(\hbox {PM}_{2.5}\) data at two Southeastern US locations, Columbia, SC and Tampa, FL, where we estimate the coefficient functions for the APVs corresponding to both ‘typical’ and ‘high’ \(\hbox {PM}_{2.5}\) events. As we believe that the true coefficient functions are smooth and may be exactly zero over subsets of their domains, we impose penalties on the 0th and 2nd derivatives. Our analysis indicates that the corresponding atmospheric conditions differ between the two locations, and that the conditions differ seasonally within location.