臺灣博碩士論文加值系統

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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 stratifiedbeforehand. We discuss their performances based on mean squared error through pertinent mathematical expression and Monte Carlo simulation. Additionally, ACS is arelatively new sampling design which is different from the conventional probability sampling designs in the sense that the selection of sampling units depends on the observationsobtained during the survey. It can provide more efficient estimates than the comparable conventional sampling design, especially for rare or clustered population. To utilize anauxiliary 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 theseestimators by Rao-Blackwellization technique. Different Rao-Blackwellized versions of ratio estimator will be proposed in the second part of this thesis. The improvement willbe examined via simulation study. Finally, suggestions of how to properly utilize the auxiliary variable in practice will be discussed.
 1 Introduction ...12 Ratio Estimation, Regression Estimation and Post- stratification ...62.1 Ratio Estimation ...72.2 Regression Estimation ...102.3 Post-stratification ...122.4 Comparison ...153 Monte Carlo Simulation Study I ...174 Ratio Estimations on Adaptive Cluster Sampling ...224.1 Adaptive Cluster Sampling ...224.2 Ratio Estimations on ACS ...254.2.1 Traditional Ratio Estimation on ACS ...264.2.2 Generalized Ratio Estimation on ACS ...265 Rao-Blackwellized Ratio Estimations on Adaptive Cluster Sampling ...285.1 Univariate Estimations ...285.1.1 Conditional on a Minimal Sufficient Statistic ...295.1.2 Conditional on a Sufficient Statistic ...325.2 Rao-Blackwellized Ratio Estimations ...336 Monte Carlo Simulation Study II ...367 Final Comments ...39References ...42