Smoothing quantile regressions

Understand

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.