  The weak convergence of the quantile processes, which are constructed based
on different estimators of the finite population quantiles, is shown under
various well-known sampling designs based on a superpopulation model. The
results related to the weak convergence of these quantile processes are applied
to find asymptotic distributions of the smooth $L$-estimators and the
estimators of smooth functions of finite population quantiles. Based on these
asymptotic distributions, confidence intervals are constructed for several
finite population parameters like the median, the $\alpha$-trimmed means, the
interquartile range and the quantile based measure of skewness. Comparisons of
various estimators are carried out based on their asymptotic distributions. We
show that the use of the auxiliary information in the construction of the
estimators sometimes has an adverse effect on the performances of the smooth
$L$-estimators and the estimators of smooth functions of finite population
quantiles under several sampling designs. Further, the performance of each of
the above-mentioned estimators sometimes becomes worse under sampling designs,
which use the auxiliary information, than their performances under simple
random sampling without replacement (SRSWOR).
