Yadav Subhash Kumar, Vishwakarma Gajendra K, Sharma Dinesh K
Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, 226025, India.
Department of Mathematics and Computing, Indian Institute of Technology (ISM) Dhanbad, Dhanbad, 826004, India.
Sci Rep. 2024 Mar 18;14(1):6433. doi: 10.1038/s41598-024-57264-y.
In this study, we suggest an optimal imputation strategy for the elevated estimation of the population mean of the primary variable utilizing the known auxiliary parameters for the missing observations. Under this strategy, we suggest a new modified Searls type estimator, and we study its sampling properties, mainly bias and mean squared error (MSE), for an approximation of order one. The introduced estimator is compared theoretically with the estimators of population mean in competition under the imputation method. The efficiency conditions for the introduced estimator to be more efficient than the estimators in the competition are derived. To be sure about the efficiencies, these efficiency conditions are verified through the three natural populations. We have also conducted a simulation study and generated an artificial population with the same parameters as a natural population. The estimator with minimum MSE and the highest Percentage Relative Efficiency (PRE) is recommended for practical use in different areas of applications.
在本研究中，我们提出了一种最优插补策略，用于利用缺失观测值的已知辅助参数来提高主要变量总体均值的估计。在该策略下，我们提出了一种新的改进的塞尔尔斯型估计量，并研究了其一阶近似的抽样性质，主要是偏差和均方误差（MSE）。将引入的估计量与插补方法下竞争的总体均值估计量进行理论比较。推导了引入的估计量比竞争估计量更有效的效率条件。为了确定效率，通过三个自然总体验证了这些效率条件。我们还进行了模拟研究，并生成了一个与自然总体参数相同的人工总体。建议使用具有最小MSE和最高相对效率百分比（PRE）的估计量，以便在不同应用领域实际使用。
