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研究生:江姿青
研究生(外文):Tzu-Ching Chiang
論文名稱:輔助訊息對抽樣調查之影響研究
論文名稱(外文):Issues of Auxiliary Information on Sampling Survey
指導教授:趙昌泰趙昌泰引用關係
指導教授(外文):Chang-Tai Chao
學位類別:碩士
校院名稱:國立成功大學
系所名稱:統計學系碩博士班
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:英文
論文頁數:43
中文關鍵詞:Hansen-Hurwitz 估計Horvitz-Thompson 估計Rao-Blackwellization調適型集群抽樣輔助變數設計觀點之抽樣策略事後分層比例估計迴歸估計相對有效性
外文關鍵詞:Auxiliary variableAdaptive Cluster SamplingHansen-Hurwitz estimationDesign-based sampling strategyHorvitz-Thompson estimationRegression estimationPost-stratificationRatio estimationRao-BlackwellizationRelative efficiency
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在許多的抽樣情況中,研究者不僅可以收集到所感興趣的主要變數,額外的輔助訊息也常伴隨著被觀察。在抽樣研究中,輔助變數可以被使用於抽樣設計與推論上,用以提升估計精確度的常見方法。適當的使用輔助變數,將提供更有效率且較精確的推論。本文將分別在簡單隨機抽樣和調適型集群抽樣兩種抽樣設計下,討論如何有效地運用輔助變數,以提升推論的精確性。在簡單隨機抽樣設計中,比例估計與迴歸估計利用主要變數與輔助變數的關聯性於推論中,是經常被使用
的估計方法。在另外一方面,事後分層也是一種當調查母體無法進行事前分層時,經常被建議的估計方法,因此本文第一部分,將分別以理論與模擬的方式,比較這三種估計方法的估計均方誤,並提出各自較適用的時機與條件。另一方面,由於 Chao (2004),Dryver 與 Chao(2007) 提出適用於調適型集群抽樣的比例估計式,並非最小充分統計量的函數。因此這些估計量是可以更進一步加以改進以求得更好的推論結果,於本文的第二部分, 將利用 Rao-Blackwellization 提出四種改進的比例估計式,並利用蒙地卡羅模擬法衡量此四種估計式的改善能力,進而從中找出於調適型集群抽樣中,當輔助訊息存在時更有效的估計方法。
In many sampling situations, the investigations often collect data from more than one variables, including the variable of primary interest and auxiliary variables. In order to make the best use of survey data, we discuss how to utilize auxiliary information in the estimation of population quantity of interest under two different sampling designs; Simple Random Sampling without Replacement (SRSWOR) and Adaptive Cluster Sampling (ACS). In SRSWOR, ratio and regression estimations are two well-known estimation methods which take advantage of the correlation between the variable of interest and the auxiliary variable. On the other hand, post-stratification is another estimation methods widely used in practice, especially when the population cannot be stratified
beforehand. We discuss their performances based on mean squared error through pertinent mathematical expression and Monte Carlo simulation. Additionally, ACS is a
relatively new sampling design which is different from the conventional probability sampling designs in the sense that the selection of sampling units depends on the observations
obtained during the survey. It can provide more efficient estimates than the comparable conventional sampling design, especially for rare or clustered population. To utilize an
auxiliary variable under ACS, various ACS types of ratio estimators have been proposed by Chao (2004) and Dryver and Chao (2007). It is possible to further improve these
estimators by Rao-Blackwellization technique. Different Rao-Blackwellized versions of ratio estimator will be proposed in the second part of this thesis. The improvement will
be examined via simulation study. Finally, suggestions of how to properly utilize the auxiliary variable in practice will be discussed.
1 Introduction ...1
2 Ratio Estimation, Regression Estimation and Post- stratification ...6
2.1 Ratio Estimation ...7
2.2 Regression Estimation ...10
2.3 Post-stratification ...12
2.4 Comparison ...15
3 Monte Carlo Simulation Study I ...17
4 Ratio Estimations on Adaptive Cluster Sampling ...22
4.1 Adaptive Cluster Sampling ...22
4.2 Ratio Estimations on ACS ...25
4.2.1 Traditional Ratio Estimation on ACS ...26
4.2.2 Generalized Ratio Estimation on ACS ...26
5 Rao-Blackwellized Ratio Estimations on Adaptive Cluster Sampling ...28
5.1 Univariate Estimations ...28
5.1.1 Conditional on a Minimal Sufficient Statistic ...29
5.1.2 Conditional on a Sufficient Statistic ...32
5.2 Rao-Blackwellized Ratio Estimations ...33
6 Monte Carlo Simulation Study II ...36
7 Final Comments ...39
References ...42
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Dryver, A.L., and Thompson, S.K. (2005). Improved unbiased estimators in adaptive cluster sampling. Journal of the Royal Statistical Society B, 67, 157–166.

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