  We propose to smooth the entire objective function, rather than only the
check function, in a linear quantile regression context. Not only does the
resulting smoothed quantile regression estimator yield a lower mean squared
error and a more accurate Bahadur-Kiefer representation than the standard
estimator, but it is also asymptotically differentiable. We exploit the latter
to propose a quantile density estimator that does not suffer from the curse of
dimensionality. This means estimating the conditional density function without
worrying about the dimension of the covariate vector. It also allows for
two-stage efficient quantile regression estimation. Our asymptotic theory holds
uniformly with respect to the bandwidth and quantile level. Finally, we propose
a rule of thumb for choosing the smoothing bandwidth that should approximate
well the optimal bandwidth. Simulations confirm that our smoothed quantile
regression estimator indeed performs very well in finite samples.
