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Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion

机译：基于EdgeWorth扩展的有限人口总数的非参数估计器

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摘要

In survey sampling, the main objective is to make inference about the entire population parameters using the sample statistics. In this study, a nonparametric estimator of finite population total is proposed and the coverage probabilities using the Edgeworth expansion explored. Three properties; unbiasedness, efficiency and the confidence interval of the proposed estimator are studied. There is a lot of literature on study of two properties; unbiasedness and efficiency of the finite population total. This study therefore has more focus on confidence interval and coverage probability. The amount of bias and MSE are studied partially analytically, followed by an empirical study on the two properties and the confidence interval of the proposed estimator. Based on the empirical study with simulations in R, the proposed estimator resulted into smaller bias and MSE compared to the nonparametric estimator due to [6], the design-based Horvitz-Thompson estimator and the model-based ratio estimator. Further, the proposed estimator is tighter compared to the other three considered in this study and has higher converging coverage probabilities.
机译：在调查采样中，主要目标是使用样本统计来推断整个人口参数。在本研究中，提出了有限人口总量的非参数估计，并使用EdgeWorth扩展探索的覆盖概率。三个属性;研究了所提出的估计者的无偏见，效率和置信区间。有很多关于两个物业的文学;有限人口的无偏见和效率。因此，该研究更加注重置信区间和覆盖概率。部分分析地研究了偏差和MSE的量，然后进行了对所提出的估计器的两个性质和置信区分的实证研究。基于r的模拟的实证研究，所提出的估计器与[6]，基于设计的Horvitz-Thompson估计和基于模型的比率估计器相比，与非参数估计器相比，偏差和MSE较小。此外，与本研究中考虑的其他三个相比，所提出的估计器更加紧张，并且具有更高的会聚覆盖概率。

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