Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan.
Department of Statistics, Government College University, Lahore, Pakistan.
PLoS One. 2020 Dec 17;15(12):e0243584. doi: 10.1371/journal.pone.0243584. eCollection 2020.
In this paper, we propose two new families of estimators for estimating the finite population distribution function in the presence of non-response under simple random sampling. The proposed estimators require information on the sample distribution functions of the study and auxiliary variables, and additional information on either sample mean or ranks of the auxiliary variable. We considered two situations of non-response (i) non-response on both study and auxiliary variables, (ii) non-response occurs only on the study variable. The performance of the proposed estimators are compared with the existing estimators available in the literature, both theoretically and numerically. It is also observed that proposed estimators are more precise than the adapted distribution function estimators in terms of the percentage relative efficiency.
在本文中，我们提出了两种新的估计器家族，用于在简单随机抽样下存在无回应的情况下估计有限总体分布函数。所提出的估计器需要关于研究和辅助变量的样本分布函数的信息，以及关于辅助变量的样本均值或等级的附加信息。我们考虑了两种无回应情况：（i）研究和辅助变量都无回应，（ii）仅研究变量无回应。从理论和数值两方面对所提出的估计器与文献中现有的估计器进行了比较。还观察到，在所提出的估计器中，相对于适应分布函数估计器，在百分比相对效率方面，所提出的估计器更精确。
