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

【摘要】：在實(shí)際調(diào)查研究中,常常有必要得知研究總體所關(guān)心指標(biāo)的總體特性,如研究變量總值、均值等.簡單估計(jì)固然簡單,但常伴隨著估計(jì)量精度不高,當(dāng)存在缺失數(shù)據(jù)情形時(shí),更是如此.以提高已有總體參數(shù)的估計(jì)量精度為目標(biāo)的改進(jìn)研究是一個(gè)不斷深入的課題.大量文獻(xiàn)指出,有效運(yùn)用輔助信息可以提高調(diào)查精度.當(dāng)存在已知的、可利用的輔助信息時(shí),不等概率抽樣設(shè)計(jì)下估計(jì)量精度較高,其中n=2時(shí)嚴(yán)格πps抽樣設(shè)計(jì)是典型的不放回不等概率抽樣.如何實(shí)施n=2時(shí)的嚴(yán)格πps抽樣設(shè)計(jì),并計(jì)算該設(shè)計(jì)下的一階、二階入樣概率等問題,是本文展開研究的另一個(gè)內(nèi)容.首先,在現(xiàn)實(shí)調(diào)查中,常常可以獲得已知的輔助信息,當(dāng)與研究變量呈正相關(guān)關(guān)系時(shí).合理運(yùn)用這些輔助信息,如總體均值、變異系數(shù)、峰度系數(shù)、偏度系數(shù)、相關(guān)系數(shù)等,可以對提高估計(jì)量的精度起到很大幫助.由于記錄員大意、個(gè)人不肯吐露信息等原因,抽樣調(diào)查常常不可避免的遇到數(shù)據(jù)缺失的情況.本文將基于含缺失數(shù)據(jù)情況時(shí),利用輔助變量的峰度系數(shù)、偏度系數(shù)提出了一系列總體均值估計(jì)量,并利用泰勒級數(shù)展開求得提出估計(jì)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(biāo)準(zhǔn),從理論上比較了提出估計(jì)和已有估計(jì)的優(yōu)劣性,獲得了優(yōu)于已有估計(jì)的條件,并基于公式和蒙特卡羅模擬驗(yàn)證了這些估計(jì)量的有效性.其次,受到Deshpande and Prabhu(1982)提出設(shè)計(jì)的思想啟發(fā),本文構(gòu)造了一種新的n=2時(shí)的嚴(yán)格πps抽樣設(shè)計(jì).當(dāng)輔助單元大小符合1 2iX X(27)時(shí),提出的新設(shè)計(jì)不僅容易實(shí)施,而且一階和二階入樣概率計(jì)算簡單.此外,本文還獲得了H-T估計(jì)量的一個(gè)非負(fù)的方差估計(jì).通過數(shù)值比較提出設(shè)計(jì)和嚴(yán)格πps抽樣設(shè)計(jì),說明提出方法具有潛在應(yīng)用價(jià)值.最后,由本文提出的新的n=2時(shí)嚴(yán)格πps抽樣設(shè)計(jì)出發(fā),建立每層采用n=2時(shí)嚴(yán)格πps抽樣的分層抽樣理論,并基于實(shí)際數(shù)據(jù)集評價(jià)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(xué)位授予單位】：內(nèi)蒙古工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.2

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相關(guān)期刊論文 前2條

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本文編號：2077816