  In this manuscript, we study quantile regression in partial functional linear
model where response is scalar and predictors include both scalars and multiple
functions. Wavelet basis are adopted to better approximate functional slopes
while effectively detect local features. The sparse group lasso penalty is
imposed to select important functional predictors while capture shared
information among them. The estimation problem can be reformulated into a
standard second-order cone program and then solved by an interior point method.
We also give a novel algorithm by using alternating direction method of
multipliers (ADMM) which was recently employed by many researchers in solving
penalized quantile regression problems. The asymptotic properties such as the
convergence rate and prediction error bound have been established. Simulations
and a real data from ADHD-200 fMRI data are investigated to show the
superiority of our proposed method.
