  For the kernel estimator of the quantile density function (the derivative of
the quantile function), I show how to perform the boundary bias correction,
establish the rate of strong uniform consistency of the bias-corrected
estimator, and construct the confidence bands that are asymptotically exact
uniformly over the entire domain $[0,1]$. The proposed procedures rely on the
pivotality of the studentized bias-corrected estimator and known
anti-concentration properties of the Gaussian approximation for its supremum.
