Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan.
Department of Applied Statistics, Financial Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, Bondo, Kenya.
PLoS One. 2022 Jul 1;17(7):e0270277. doi: 10.1371/journal.pone.0270277. eCollection 2022.
In this study, we propose an improved unbiased estimator in estimating the finite population mean using a single auxiliary variable and rank of the auxiliary variable by adopting the Hartley-Ross procedure when some parameters of the auxiliary variable are known. Expressions for the bias and mean square error or variance of the estimators are obtained up to the first order of approximation. Four real data sets are used to observe the performances of the estimators and to support the theoretical findings. It turns out that the proposed unbiased estimator outperforms as compared to all other considered estimators. It is also observed that using conventional measures have significant contributions in achieving the efficiency of the estimators.
在这项研究中，我们提出了一种改进的无偏估计量，用于在某些辅助变量的参数已知的情况下，通过采用 Hartley-Ross 程序，使用单个辅助变量和辅助变量的秩来估计有限总体均值。我们得到了直到一阶近似的估计量的偏差和均方误差或方差的表达式。使用四个真实数据集来观察估计量的性能并支持理论发现。结果表明，与所有其他考虑的估计量相比，所提出的无偏估计量表现更好。还观察到，使用常规措施对实现估计量的效率有重要贡献。
