  We establish a functional limit law of the logarithm for the increments of
the normed quantile process based upon a random sample of size $n\to\infty$. We
extend a limit law obtained by Deheuvels and Mason (12), showing that their
results hold uniformly over the bandwidth $h$, restricted to vary in
$[h'_n,h''_n]$, where $\{h'_n\}_{n\geq1}$ and $\{h''_n\}_{n\geq 1}$ are
appropriate non-random sequences. We treat the case where the sample
observations follow possibly non-uniform distributions. As a consequence of our
theorems, we provide uniform limit laws for nearest-neighbor density
estimators, in the spirit of those given by Deheuvels and Mason (13) for
kernel-type estimators.
