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研究生：	林翊涵 Lin, Yi-Han
論文名稱：	基於傳統多變量分析方法之模型觀點抽樣設計 A Model-Based Sampling Selection Method Based on Classical Multivariate Analysis Methods
指導教授：	趙昌泰 Chao, Chang-Tai
學位類別：	碩士 Master
系所名稱：	管理學院 - 統計學系 Department of Statistics
論文出版年：	2018
畢業學年度：	106
語文別：	英文
論文頁數：	94
中文關鍵詞：	典型相關分析、樣本調整、模型觀點抽樣理論
外文關鍵詞：	Canonical Correlation Analysis, Sample Adjustment, Model-based Sampling
相關次數：	點閱：179 下載：9
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抽樣調查時，收集每一個樣本都需要一定的成本，因此在固定的總樣本數下，該如何選取較具有代表性的樣本是抽樣理論及應用中的基本問題。在一些抽樣方法中，如分層抽樣，會先將母體分成數層，並對各層進行樣本數配置，但在樣本數配置過程中會出現問題，舉例來說，各層樣本數有時不是一個整數，或是在某些情況下分配到的樣本數為零，這時需要對層內樣本數做四捨五入取至整數位，或是進行調整，但四捨五入或調整過後的總樣本數往往不是原先所給定的，故在先前研究中會使用隨機抽樣來去除多餘或是添補缺漏的樣本。
在本研究中，基於多變量分析方法的典型相關分析，提出兩種抽樣策略來調整樣本。延續先前趙昌泰(2004)和趙昌泰與林楓敏(2007)所提出選取樣本的方法，在已知母體共變異數矩陣及給定之總樣本數下，使用群集分析將母體分群並做樣本數配置，接著根據四捨五入或調整過後的樣本數利用主成分分析進行群內樣本選取，最後當四捨五入或調整過後的總樣本數與原先所給定的不同時再調整樣本。這兩種抽樣策略不需要完整的母體模型假設，僅需要母體共變異數矩陣，即可選取適當的樣本進行調整。透過多種模擬研究和三個實際資料應用，證明所提出的抽樣策略優於簡單隨機抽樣和之前所提出方法的預測結果，在固定的樣本數下使用這兩種抽樣策略選取樣本可以最小化均方預測誤差，且不需要複雜的演算法與繁重的計算負載，在實際應用上能更加彈性和簡單。

In survey sampling, it takes a certain cost to collect each sampling unit. Therefore, given a fixed total sample size, how to select a more representative sample is the basic problem in sampling theory and application. In some sampling designs, such as stratified sampling, the population is firstly divided into several layers, and then the sample size is allocated to each layer. However, there is a problem in the process of sample size allocation. For example, sample size in each layer usually is not an integer and in some cases, sample size will be zero. At that time, the sample size in each layer needs to be rounded to the nearest integer or be adjusted. Nevertheless, the total sample size after rounding and/or adjustment is often not the same as the given one. Therefore, in previous researches, random sampling is used to remove excess sampling units or add missing ones.
In this research, based on canonical correlation analysis in multivariate analysis techniques, two model-based sampling strategies are proposed to adjust the sample. It extends the sampling methods proposed by Chao (2004) and Chao and Lin (2007). Under the known population covariance matrix and the given total sample size, one may use cluster analysis to partition the population into several clusters and do the sample size allocation. Then, one may utilize principal component analysis to select the within-cluster sample on the basis of the sample size after rounding and/or adjustment. Finally, select the adjusted sample when the total sample size after rounding and/or adjustment is different from the given one. These two sampling designs do not need an exact population distribution, but a population covariance matrix, and an appropriate sample can be selected for adjustment. Multiple simulation studies and three applications of actual data show that proposed sampling strategies perform better prediction results than that of simple random sampling without replacement and methods proposed in the past. Under a fixed total sample size, selecting sampling units by these two sampling strategies can minimize the mean-squared prediction error. No complicated algorithm and intensive computational load are required. It is more flexible and simple to implement the procedures in practice.

摘要.............................................i
Abstract........................................ii
誌謝...........................................iii
Table of Contents...............................iv
List of Tables..................................vi
List of Figures................................vii
Chapter 1. Introduction..........................1
Chapter 2. Sampling Design.......................4
  2.1. Cluster Analysis..........................5
  2.2. Principal Component Analysis..............6
    2.2.1. EigenSamp 1...........................6
    2.2.2. EigenSamp 2...........................6
  2.3. Canonical Correlation Analysis............7
    2.3.1. Definition............................8
    2.3.2. Design 1..............................9
    2.3.3. Design 2.............................10
Chapter 3. Simulation Studies...................13
  3.1. Population Models........................13
    3.1.1. Gaussian model.......................13
    3.1.2. log-Gaussian model...................15
  3.2. Sampling Locations.......................16
  3.3. Predictors for Population Total and Relative Efficiency to SRSWOR.....19
  3.4. Simulation Results.......................20
    3.4.1. Gaussian population model............21
    3.4.2. log-Gaussian population model........25
Chapter 4. Data Applications....................31
  4.1. Rainfall in Yunlin, Chiayi and Tainan for August, 2017.....31
    4.1.1. Population model.....................32
    4.1.2. Sampling locations...................34
    4.1.3. Application results..................35
  4.2. Average Rainfall in Parana State, Brasil.....37
    4.2.1. Population model.....................37
    4.2.2. Sampling locations...................39
    4.2.3. Application results..................40
  4.3. PM2.5 in Western Taiwan for December, 2016.....42
    4.3.1. Population model.....................42
    4.3.2. Sampling locations...................44
    4.3.3. Application results..................47
Chapter 5. Discussion and Conclusion............50
References......................................52
Appendix A. Other Results for Simulation Studies used EigenSamp 2.....53
  A.1. Using a Geometric Anisotropic Type of Gaussian-shaped Spatial Covariance Function.....53
    A.1.1. Gaussian population model............53
    A.1.2. log-Gaussian population model........55
  A.2. Using a Geometric Zonal Anisotropic Type of Gaussian-shaped Spatial Covariance Function.....59
    A.2.1. Gaussian population model............59
    A.2.2. log-Gaussian population model........61
Appendix B. Results for Simulation Studies used EigenSamp 1.....65
  B.1. Using an Isotropic Type of Gaussian-shaped Spatial Covariance Function.....65
    B.1.1. Gaussian population model............65
    B.1.2. log-Gaussian population model........67
  B.2. Using a Geometric Anisotropic Type of Gaussian-shaped Spatial Covariance Function.....71
    B.2.1. Gaussian population model............71
    B.2.2. log-Gaussian population model........73
  B.3. Using a Geometric Zonal Anisotropic Type of Gaussian-shaped Spatial Covariance Function.....77
    B.3.1. Gaussian population model............77
    B.3.2. log-Gaussian population model........79
Appendix C. Data for Applications...............83
  C.1. Data of Rainfall in Yunlin, Chiayi and Tainan for August, 2017.....83
  C.2. Data of Average Rainfall in Parana State, Brasil.....85
  C.3. Data of PM2.5 in Western Taiwan for December, 2016.....87
  C.4. Data of Weather and Air Quality Monitoring Stations in Western Taiwan.....88
  C.5. Introduction of Variables in Data of Weather and Air Quality Monitoring Stations in Western Taiwan.....90
Appendix D. Results for Data Applications used EigenSamp 1.....91
  D.1. Results of Rainfall in Yunlin, Chiayi and Tainan for August, 2017.....91
  D.2. Results of Average Rainfall in Parana State, Brasil.....92
  D.3. Results of PM2.5 in Western Taiwan for December, 2016.....93
    D.3.1. BLUP.................................93
    D.3.2. BUP..................................94
                                    

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校內：2023-08-01公開
校外：2023-08-01公開

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