Hussain Muhammad Ali, Javed Maria, Zohaib Muhammad, Shongwe Sandile C, Awais Muhammad, Zaagan Abdullah A, Irfan Muhammad
Business School, NingboTech University, Ningbo, 315100, Zhejiang, China.
Department of Statistics, Government College University, Faisalabad, Pakistan.
Heliyon. 2024 Mar 30;10(7):e28891. doi: 10.1016/j.heliyon.2024.e28891. eCollection 2024 Apr 15.
To estimate the unknown population median, several researchers have developed efficient estimators but these estimators are unable to provide efficient results in the existence of outliers. Keeping this point in view, the present work suggests enhanced class of robust estimators to estimate population median under simple random sampling in case of outliers/extreme observations. The suggested estimators are a mixture of bivariate auxiliary information and robust measures with the linear combination of deciles mean, tri-mean and Hodges Lehmann estimator. Mathematical properties associated with the improved class of robust estimators are evaluated in terms of bias and mean squared error. Moreover, the potentiality of our suggested estimators as compared to already available estimators is checked by considering two real-life data sets with outlier(s). In addition, a simulation study is also added in this regard. From theoretical and numerical findings, it is observed that our newly suggested estimators outperforms as compared to its competitors.
为了估计未知的总体中位数，几位研究人员开发了有效的估计量，但在存在异常值的情况下，这些估计量无法提供有效的结果。鉴于这一点，本研究提出了一类增强的稳健估计量，用于在存在异常值/极端观测值的情况下，在简单随机抽样中估计总体中位数。所提出的估计量是双变量辅助信息和稳健度量的混合，与十分位数均值、三均值和霍奇斯·莱曼估计量的线性组合。从偏差和均方误差的角度评估了与改进后的稳健估计量类相关的数学性质。此外，通过考虑两个包含异常值的实际数据集，检验了我们提出的估计量与已有估计量相比的潜力。此外，在这方面还增加了一项模拟研究。从理论和数值结果可以看出，我们新提出的估计量比其竞争对手表现更优。
