缺失数据下总体均值估计和n=2时严格πps抽样设计

发布时间：2018-06-28 11:16

本文选题：辅助变量 + H-T估计量　；参考：《内蒙古工业大学》2017年硕士论文

【摘要】：在实际调查研究中,常常有必要得知研究总体所关心指标的总体特性,如研究变量总值、均值等.简单估计固然简单,但常伴随着估计量精度不高,当存在缺失数据情形时,更是如此.以提高已有总体参数的估计量精度为目标的改进研究是一个不断深入的课题.大量文献指出,有效运用辅助信息可以提高调查精度.当存在已知的、可利用的辅助信息时,不等概率抽样设计下估计量精度较高,其中n=2时严格πps抽样设计是典型的不放回不等概率抽样.如何实施n=2时的严格πps抽样设计,并计算该设计下的一阶、二阶入样概率等问题,是本文展开研究的另一个内容.首先,在现实调查中,常常可以获得已知的辅助信息,当与研究变量呈正相关关系时.合理运用这些辅助信息,如总体均值、变异系数、峰度系数、偏度系数、相关系数等,可以对提高估计量的精度起到很大帮助.由于记录员大意、个人不肯吐露信息等原因,抽样调查常常不可避免的遇到数据缺失的情况.本文将基于含缺失数据情况时,利用辅助变量的峰度系数、偏度系数提出了一系列总体均值估计量,并利用泰勒级数展开求得提出估计量的均方误差和偏倚公式.另外以均方误差作为精度的刻画标准,从理论上比较了提出估计和已有估计的优劣性,获得了优于已有估计的条件,并基于公式和蒙特卡罗模拟验证了这些估计量的有效性.其次,受到Deshpande and Prabhu(1982)提出设计的思想启发,本文构造了一种新的n=2时的严格πps抽样设计.当辅助单元大小符合1 2iX X(27)时,提出的新设计不仅容易实施,而且一阶和二阶入样概率计算简单.此外,本文还获得了H-T估计量的一个非负的方差估计.通过数值比较提出设计和严格πps抽样设计,说明提出方法具有潜在应用价值.最后,由本文提出的新的n=2时严格πps抽样设计出发,建立每层采用n=2时严格πps抽样的分层抽样理论,并基于实际数据集评价其精度。
[Abstract]:In the actual investigation and research, it is often necessary to know the overall characteristics of the indicators concerned in the study, such as the total value of the study variables, the mean value, and so on. Simple estimation is simple, but it is often accompanied by low accuracy of estimator, especially when there are missing data. The research on improving the precision of existing parameters estimation is a deep topic. A large number of documents point out that the effective use of auxiliary information can improve the accuracy of the investigation. When there is known and available auxiliary information, the estimator accuracy is higher under unequal probability sampling design, where n = 2 strictly 蟺 PS sampling design is a typical non-return unequal probability sampling. How to implement the strict 蟺 PS sampling design with n = 2 and calculate the first and second order sampling probability is another content of this paper. First of all, in the actual investigation, we can obtain the known auxiliary information, when there is a positive correlation with the research variables. The reasonable use of these auxiliary information, such as the total mean, variation coefficient, kurtosis coefficient, skewness coefficient, correlation coefficient and so on, can greatly help to improve the accuracy of the estimator. Because of the carelessness of the recorder and the refusal of the individual to disclose information, the sampling survey often encounters the lack of data inevitably. In this paper, a series of estimators of the total mean are proposed by using the kurtosis and skewness coefficients of auxiliary variables in the case of missing data, and the formulas of mean square error and bias of the estimators are obtained by Taylor series expansion. In addition, with the mean square error as the criterion of accuracy, the advantages and disadvantages of the proposed estimates and the existing estimates are compared theoretically, and the conditions superior to the existing estimates are obtained. The validity of these estimators is verified based on the formulas and Monte Carlo simulations. Secondly, inspired by the idea of design proposed by Deshpande and Prabhu (1982), a new strict 蟺 PS sampling design with n = 2 is constructed. When the size of the auxiliary unit is in accordance with the size of 12x X (27), the proposed new design is not only easy to implement, but also simple to calculate the first and second order sampling probability. In addition, a nonnegative variance estimate of H-T estimator is obtained. Through numerical comparison and strict 蟺 PS sampling design, it is shown that the proposed method has potential application value. Finally, based on the new strict 蟺 PS sampling design proposed in this paper, the stratified sampling theory of n = 2 strict 蟺 PS sampling for each layer is established, and its accuracy is evaluated based on the actual data set.
【学位授予单位】：内蒙古工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.2

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