Azeem Muhammad, Salahuddin Najma, Hussain Sundus, Ijaz Musarrat, Salam Abdul
Department of Statistics, University of Malakand, Khyber Pakhtunkhwa, Pakistan.
Department of Statistics, Shaheed Benazir Bhutto Women University, Peshawar, Pakistan.
Heliyon. 2024 Mar 6;10(5):e27488. doi: 10.1016/j.heliyon.2024.e27488. eCollection 2024 Mar 15.
In sampling theory, a majority of the available estimators of population variance are designed for use with non-sensitive variables only. Such estimators cannot perform efficiently when the variable of interest is of sensitive nature, such as use of drugs, illegal income, abortion, cheating in examination, the amount of income tax payable, and the violation of rules by employees, etc. In the current literature, the shortage of research studies on variance estimators of a sensitive variable has created a big research gap and a room for improvement in the efficiency of such estimators. In this paper, a new randomized scrambling technique is proposed, along with a new estimator of population variance. The new estimator achieves improvement in efficiency over the available variance estimators. The proposed estimator is designed for use with simple random sampling and uses the information on an auxiliary variable. The improvement in efficiency is shown for different choices of constants. Besides efficiency, improvement in the unified measure of estimator quality is also achieved with the proposed estimator under the new randomized response model.
在抽样理论中，大多数现有的总体方差估计量仅设计用于非敏感变量。当感兴趣的变量具有敏感性质时，如药物使用、非法收入、堕胎、考试作弊、应缴纳所得税金额以及员工违规等，此类估计量无法有效发挥作用。在当前文献中，关于敏感变量方差估计量的研究不足造成了巨大的研究空白，也为提高此类估计量的效率提供了改进空间。本文提出了一种新的随机加扰技术以及一种新的总体方差估计量。新估计量在效率上优于现有的方差估计量。所提出的估计量设计用于简单随机抽样，并利用辅助变量的信息。针对不同的常数选择展示了效率的提高。除了效率之外，在所提出的估计量在新的随机化回答模型下，估计量质量的统一度量也得到了改进。
