List of abbreviations and acronyms

This study focuses on estimating a finite population cumulative distribution function (CDF) using two-stage and three-stage cluster sampling under non-response. This work is then extended to estimate the finite population CDF under non-response using stratified two-stage and three-stage cluster sampling. We propose two distinct families of CDF estimators, specifically designed for these complex surveys, namely classical ratio/product-type and exponential ratio/product-type. Furthermore, we introduce a difference estimator for the CDF under non-response, utilizing ancillary information about the variances and covariances of the estimators under these complex schemes. We provide mathematical expressions for the biases and mean squared errors of the proposed CDF estimators, based on first-order approximation. To evaluate the performance of the proposed estimators, we conduct extensive simulations and assess their efficiency. The simulation results demonstrate that the proposed families of estimators perform well under different sampling scenarios. Our findings indicate that difference CDF estimators are more explicit than the other estimators discussed. We support our theoretical claims by analyzing real datasets.

本研究聚焦于无应答情形下，采用两阶段与三阶段整群抽样对有限总体累积分布函数（cumulative distribution function, CDF）进行估计。后续将研究拓展至分层两阶段与三阶段整群抽样场景下，无应答情形的有限总体CDF估计问题。本文提出两类专为这类复杂抽样设计打造的CDF估计量族，即经典比/积型估计量族与指数比/积型估计量族。此外，本文还针对无应答情形下的CDF估计问题引入差分估计量，借助基于上述复杂抽样方案的估计量方差与协方差辅助信息。基于一阶近似理论，本文推导了所提CDF估计量的偏倚与均方误差的数学表达式。为评估所提估计量的性能，本文开展了大规模模拟实验并对各估计量的效率进行评估。模拟结果表明，所提出的估计量族在不同抽样场景下均表现优异。研究结果显示，差分CDF估计量相较于文中讨论的其他估计量，性能更为突出。本文通过分析真实数据集，佐证了理论推导的合理性。