本文選題：輔助變量 + H-T估計量��； 參考：《內蒙古工業(yè)大學》2017年碩士論文

【摘要】：在實際調查研究中,常常有必要得知研究總體所關心指標的總體特性,如研究變量總值、均值等.簡單估計固然簡單,但常伴隨著估計量精度不高,當存在缺失數據情形時,更是如此.以提高已有總體參數的估計量精度為目標的改進研究是一個不斷深入的課題.大量文獻指出,有效運用輔助信息可以提高調查精度.當存在已知的、可利用的輔助信息時,不等概率抽樣設計下估計量精度較高,其中n=2時嚴格πps抽樣設計是典型的不放回不等概率抽樣.如何實施n=2時的嚴格πps抽樣設計,并計算該設計下的一階、二階入樣概率等問題,是本文展開研究的另一個內容.首先,在現(xiàn)實調查中,常�？梢垣@得已知的輔助信息,當與研究變量呈正相關關系時.合理運用這些輔助信息,如總體均值、變異系數、峰度系數、偏度系數、相關系數等,可以對提高估計量的精度起到很大幫助.由于記錄員大意、個人不肯吐露信息等原因,抽樣調查常常不可避免的遇到數據缺失的情況.本文將基于含缺失數據情況時,利用輔助變量的峰度系數、偏度系數提出了一系列總體均值估計量,并利用泰勒級數展開求得提出估計量的均方誤差和偏倚公式.另外以均方誤差作為精度的刻畫標準,從理論上比較了提出估計和已有估計的優(yōu)劣性,獲得了優(yōu)于已有估計的條件,并基于公式和蒙特卡羅模擬驗證了這些估計量的有效性.其次,受到Deshpande and Prabhu(1982)提出設計的思想啟發(fā),本文構造了一種新的n=2時的嚴格πps抽樣設計.當輔助單元大小符合1 2iX X(27)時,提出的新設計不僅容易實施,而且一階和二階入樣概率計算簡單.此外,本文還獲得了H-T估計量的一個非負的方差估計.通過數值比較提出設計和嚴格πps抽樣設計,說明提出方法具有潛在應用價值.最后,由本文提出的新的n=2時嚴格πps抽樣設計出發(fā),建立每層采用n=2時嚴格πps抽樣的分層抽樣理論,并基于實際數據集評價其精度。
[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.
【學位授予單位】：內蒙古工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O212.2

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本文編號：2077816