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).

翻译：基于超总体模型，在不同抽样设计下，本文证明了由有限总体分位数估计量构造的分位数过程的弱收敛性。利用这些分位数过程的弱收敛结果，推导了光滑$L$估计量及有限总体分位数光滑函数估计量的渐近分布。基于这些渐近分布，为有限总体中位数、$\alpha$截尾均值、四分位距及基于分位数的偏度测度等参数构建了置信区间。通过渐近分布对不同估计量进行了比较分析。研究表明，在某些抽样设计下，在估计量构建过程中引入辅助信息，可能对光滑$L$估计量及有限总体分位数光滑函数估计量的性能产生不利影响。此外，与不放回简单随机抽样（SRSWOR）相比，采用辅助信息的抽样设计有时会导致上述估计量的性能下降。