  Functional linear regression is a useful extension of simple linear
regression and has been investigated by many researchers. However, functional
variable selection problems when multiple functional observations exist, which
is the counterpart in the functional context of multiple linear regression, is
seldom studied. Here we propose a method using group smoothly clipped absolute
deviation penalty (gSCAD) which can perform regression estimation and variable
selection simultaneously. We show the method can identify the true model
consistently and discuss construction of pointwise confidence interval for the
estimated functional coefficients. Our methodology and theory is verified by
simulation studies as well as an application to spectrometrics data.
