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Estimation of Population Median under Robust Measures of an Auxiliary Variable
Mathematical Problems in Engineering ( IF 1.430 ) Pub Date : 2021-09-18 , DOI: 10.1155/2021/4839077 Muhammad Irfan 1 , Maria Javed 1 , Sandile C. Shongwe 2 , Muhammad Zohaib 1 , Sajjad Haider Bhatti 1
Mathematical Problems in Engineering ( IF 1.430 ) Pub Date : 2021-09-18 , DOI: 10.1155/2021/4839077 Muhammad Irfan 1 , Maria Javed 1 , Sandile C. Shongwe 2 , Muhammad Zohaib 1 , Sajjad Haider Bhatti 1
Affiliation
In this paper, a generalized class of estimators for the estimation of population median are proposed under simple random sampling without replacement (SRSWOR) through robust measures of the auxiliary variable. Three robust measures, decile mean, Hodges–Lehmann estimator, and trimean of an auxiliary variable, are used. Mathematical properties of the proposed estimators such as bias, mean squared error (MSE), and minimum MSE are derived up to first order of approximation. We considered various real-life datasets and a simulation study to check the potentiality of the proposed estimators over the competitors. Robustness is also examined through a real dataset. Based on the fascinating results, the researchers are encouraged to use the proposed estimators for population median under SRSWOR.
中文翻译:
辅助变量鲁棒测度下的人口中位数估计
在本文中,通过对辅助变量的稳健测量,在无替换简单随机抽样(SRSWOR)下提出了一类用于估计总体中位数的广义估计量。使用了三个稳健度量,十分位数平均值、Hodges-Lehmann 估计量和辅助变量的三均值。所提出的估计器的数学特性,例如偏差、均方误差 (MSE) 和最小 MSE,可以推导出至一阶近似值。我们考虑了各种现实生活中的数据集和模拟研究,以检查提议的估算器相对于竞争对手的潜力。还通过真实数据集检查稳健性。基于这些引人入胜的结果,我们鼓励研究人员在 SRSWOR 下使用建议的人口中位数估计量。
更新日期:2021-09-20
中文翻译:
辅助变量鲁棒测度下的人口中位数估计
在本文中,通过对辅助变量的稳健测量,在无替换简单随机抽样(SRSWOR)下提出了一类用于估计总体中位数的广义估计量。使用了三个稳健度量,十分位数平均值、Hodges-Lehmann 估计量和辅助变量的三均值。所提出的估计器的数学特性,例如偏差、均方误差 (MSE) 和最小 MSE,可以推导出至一阶近似值。我们考虑了各种现实生活中的数据集和模拟研究,以检查提议的估算器相对于竞争对手的潜力。还通过真实数据集检查稳健性。基于这些引人入胜的结果,我们鼓励研究人员在 SRSWOR 下使用建议的人口中位数估计量。