无回答与计量误差叠加时总体方差的校准估计

Calibration Estimators of Population Variance Under the Simultaneous Influence of Non-response and Measurement Errors

非抽样误差是一种系统误差,在概率抽样、非概率抽样和全面调查中都可能存在,对统计数据质量和估计结果都会造成重要影响。当前对非抽样误差视角下有限总体参数估计方法的研究存在不足,对多种非抽样误差叠加时总体方差估计的研究也比较少。文章基于校准估计方法讨论了在两种非抽样误差同时存在的情况下,分层随机抽样中有限总体方差的估计问题。针对无回答和计量误差叠加存在的情形,提出了一种改进的总体方差校准估计量。在此基础上,考察了所提校准估计量的统计性质,并推导了其偏差和均方误差的一阶近似数学表达式。模拟研究和真实数据结果均显示,所提校准估计量相比Singh的校准估计量总是更有效的。

Non-sampling error is a kind of systematic error that may exist in probability sampling,non-probability sampling and overall survey,and will have an important impact on the quality of statistical data and estimated results.At present,there are insufficient researches on the estimation of finite population parameters from the perspective of non-sampling error,and few researches on the estimation of population variance when multiple non-sampling errors are superimposed.This paper is based on the calibration estimation method to the estimation of finite population variance in stratified random sampling when the two kinds of non-sampling errors exist simultaneously,and then proposes an improved population variance calibration estimator for the case of non-response and measurement error superposition.Finally,on this basis,the paper investigates the statistical properties of the proposed calibration estimator,and deduces the first-order approximate mathematical expressions of its deviation and mean square error.Both the simulation studies and real data results show that the proposed calibration estimators are always more efficient than Singh’s standard estimators.